BILAL Basti

Souad Bounouiga

Study of Some Differential Dynamic Systems Linked to the Spread of Epidemics

Farida Bouzid

Insights into Nonlinear Diffusion Problems and Implications for Biological Systems

Rania Saadi

Mathematical Modeling for Exploring the Influence of Infectious Diseases

Aboulerbah GAWBA

Sobolev Spaces and Fourier Analysis of Tempered Distributions

Bachir BSAISSA , Taha Ghaith MAAMRIA

Techniques Mathématiques Pour Résoudre Des Problèmes Liés Aux Champs Pratiques Des EDPs Elliptiques

Oumelkheir Ahlam MAAMRI , Nourhane ARADJE

Étude Analytique De Quelques Problèmes Elliptiques Dans Des Espaces De Sobolev

Rabah Djemiat

Study of some fractional PDE models and their applications

Khedidja BEN SALEM , Meriem NASRI

Applications de la théorie des opérateurs sur les équations intégro-différentielles de Fredholm et Volterra

Radia Nour Elhouda BENOUIS

Existence de solutions continues d'équations intégrales par le théorème de Schauder

Zouhir Idriss BOUKER , Khaled BENKADDOUR

Existence de solutions auto-similaires pour quelques équations de la physique mathématiques

SILINI Khaoula

Étude d’existence de solutions auto-similaires pour une équation aux dérivées partielles non-linéaire

Nadjla BRAHIMI , Sirine RAHMANI

Étude d'existence de solutions pour quelques opérateurs d'équations intégrales linéaires

This study introduces an advanced SEIAR(H)-SI(M) model designed to analyze and understand the dynamics of cutaneous leishmaniasis transmission. The model is applied to recent health data from Algeria, focusing on M'Sila province, which has recently recorded a high disease incidence. We examine the existence, uniqueness, and stability of the solutions, as well as the basic reproduction number, equilibrium points, and their stability. The results reveal that the disease-free equilibrium is stable when the basic reproduction number is less than one, indicating that the disease can be controlled through appropriate preventive measures. Simulations show a direct correlation between transmission rates and the number of susceptible and infected individuals, emphasizing the importance of timely interventions to prevent disease outbreaks. Recommended strategies include environmental control measures, awareness campaigns, and early diagnosis and treatment protocols. This study highlights the necessity of continuously monitoring health data and adjusting model parameters to ensure its effectiveness and sustainability. The findings emphasize the importance of targeted interventions to reduce the basic reproduction number below one, thereby controlling the spread of cutaneous leishmaniasis and safeguarding public health.

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Bilal BASTI , ,(2025-12-09), Predicting Cutaneous Leishmaniasis Dynamics Through Mathematical Modeling,The Fourth National Conference in Mathematics, Biology, and Medicine (Edition 2025),University Pole of Mohamed Boudiaf - M'sila

This paper analyzes a fractional SECIR model to study infectious disease dynamics, particularly their impact on individuals with chronic conditions. We establish the existence, uniqueness, and stability of solutions under specific parameter constraints. Using Algerian health data, we estimate model parameters and demonstrate that the basic reproduction number for Tuberculosis in Algeria is below one, suggesting disease control is achievable through vaccination, treatment, and isolation measures.

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Bilal BASTI , ,(2025-11-30), Stability Analysis and Implications for Studying Tuberculosis Dynamics in Algeria,The First National Conference on Mathematical Analysis and Algebra,École Normale Supérieure de Bou-Saâda - El Moudjahid Ahmed Gaïd Salah, Algeria

This paper discusses the significance of quantum calculus in some mathematical fields. It specifically investigates solutions' existence, uniqueness, and stability for a system of n-nonlinear fractional q-differential equations with initial conditions involving Caputo fractional q-derivatives. The paper utilizes Schauder's and Banach's fixed-point theorems and Ulam-Hyers' stability criteria to explore the analytical dynamics inherent in these solutions. Additionally, it provides two illustrative examples to demonstrate the practical applicability of the obtained results.

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Bilal BASTI , , (2025-10-10), On n-nonlinear Caputo fractional q-differential systems, Filomat, Vol:39, Issue:21, pages:7383–7395, Faculty of Sciences and Mathematics, University of Nis, Serbia

This study comprehensively investigates the existence, uniqueness, and stabilityof solutions for nonlinear fractional q-differential equations involving Hilfer-Katugampolaq-derivatives of moving orders. We apply the Banach contraction principle and Schauder’sfixed-point theorem to establish the existence of solutions. Furthermore, we examine thestability of the solutions using Ulam-Hyers theorems. Two detailed examples are providedto illustrate the practical applicability and validity of our theoretical results.

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YACINE Arioua , Imane AOUINA , Bilal BASTI , , (2025-10-07), NONLINEAR FRACTIONAL Q-DIFFERENTIAL EQUATIONS INVOLVING HILFER-KATUGAMPOLA DERIVATIVES OFMOVING ORDERS, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, Vol:32, Issue:, pages:283-303, Watam Press

In this paper, we discuss and provide some analytical studies for a mathematical model of fractional-order SIRD for COVID-19 in the sense of the Caputo-Katugampola derivative. We compute and derive several stability results based on some parameters that satisfy some conditions that prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SIRD model. It does so by applying the properties of Schauder's and Banach's fixed point theorems.

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Bilal BASTI , ,(2024-12-15), Mathematical Insights to Control Epidemics Using Fractional Operators,International Conference on Mathematics and its Applications in Science and Technology,Setif 1 University Ferhat Abbas

This paper studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.

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Bilal BASTI , ,(2024-12-07), Exploring nonlinear effects in fractional reaction-diffusion/wave equations,4th National Conference of Mathematics and Applications,Mila University Center

This paper aims to investigate and derive new exact solutions for a degenerate parabolic partial differential equation, specifically a nonlinear diffusion equation that is not in divergence form. We propose an approach inspired by the traveling profile method to obtain a general form of self-similar solutions to this equation. The behavior of these solutions depends on certain parameters, which determine whether their existence is global or local in a given time T.

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Bilal BASTI , ,(2024-11-23), Traveling Profile Solutions for Parabolic Equations Describing Diffusion Phenomena,17th African Conference on Research in Computer Science and Applied Mathematics-Digital Sciences in Africa,University of Bejaia, Algeria

This study presents an innovative mathematical model denoted as the fractional SIP(H)–SI(M) model, which aims to analyze and understand the dynamics of malaria transmission and spread. This model is distinguished by incorporating memory effects through fractional differential equations, allowing for a more accurate and realistic analysis of disease spread compared to traditional models. The proposed model is applied to Algeria by estimating its parameters using recent health data (from 2000). The results revealed that the disease‐free equilibrium is stable only when the basic reproduction number is less than one, indicating that controlling the spread of malaria and possibly eradicating it can be achieved by implementing appropriate preventive measures. Simulations also demonstrated a direct correlation between the rate of infection transmission and an increase in the number of infected individuals, highlighting the need for swift action when signs of an outbreak emerge. Based on these findings, a set of preventive measures is recommended, including insecticide spraying programs, widespread distribution of insecticide‐treated bed nets, and implementation of effective treatment protocols for infected individuals. This study also emphasizes the importance of continuous monitoring of health data and updating model parameters to ensure the effectiveness and sustainability of preventive measures.

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Bilal BASTI , , (2024-11-06), Mathematical Exploration of Malaria Transmission Dynamics: Insights from Fractional Models and Numerical Simulation, Advanced Theory and Simulations, Vol:8, Issue:, pages:2400630, Wiley-VCH GmbH

This paper presents an in-depth analysis of a hybrid mathematical model, the fractional SECIR model, designed to explore the impact of infectious diseases, with particular emphasis on their effect on individuals with chronic conditions. The study delves into the existence and uniqueness of solutions for the proposed model, yielding several stability results based on parameters that adhere to specific conditions to mitigate pandemic occurrences. The model parameters were estimated using data reported by the Algerian health authorities in recent years, facilitating the application of the model to the Algerian context. The findings derived from the application of this mathematical compartmental model indicate that the basic reproduction number for certain infectious diseases in Algeria (COVID-19) is less than one. This observation suggests the potential for disease eradication or effective management through a combination of targeted interventions including vaccination, high-quality treatment, and precise isolation measures.

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Bilal BASTI , ,(2024-10-20), Analysis of fractional model for infectious diseases with a focus on chronic conditions in Algeria,The Sixth International Colloquium on Methods and Tools for Decision Support,University Mouloud Mammeri of Tizi-Ouzou, Algeria

This paper studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.

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Bilal BASTI , ,(2024-10-06), Modeling Physical Phenomena Using Fractional Partial Differential Equations,National Seminar on Modern Mathematics and Application,Mokhtar Badji University of Annaba, Algeria

This paper investigates a coupled system of nonlinear multi-term Katugampola fractional differential equations. Under sufficient conditions, it establishes the existence and uniqueness results of the solution by using standard fixed point theorems. Additionally, the paper includes some illustrative examples to strengthen the presented main results.

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Bilal BASTI , , (2024-09-12), Existence results for a coupled system of multi-term Katugampola fractional differential equations with integral conditions, Jordan Journal of Mathematics and Statistics, Vol:17, Issue:2, pages:199-209, Deanship of Scientific Research, Yarmouk University, Irbid, Jordan.

In this paper, we discuss and provide some analytical studies for a mathematical model of fractional-order SIRD for COVID-19 in the sense of the Caputo-Katugampola derivative. We compute and derive several stability results based on some parameters that satisfy some conditions which prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SIRD model. It does so by applying the properties of Schauder's and Banach's fixed point theorems.

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Bilal BASTI , ,(2024-08-23), Fractal model for predicting the spread of certain pandemics in society,The 24th International Pure Mathematics Conference 2024, Algebra, Analysis, and Geometry,University of Islamabad - Pakistan

This paper presents an in-depth analysis of a hybrid mathematical model, the fractional SECIR model, designed to explore the impact of infectious diseases, with particular emphasis on their effect on individuals with chronic conditions. The study delves into the existence and uniqueness of solutions for the proposed model, yielding several stability results based on parameters that adhere to specific conditions to mitigate pandemic occurrences. The model parameters are estimated using data reported by the Algerian health authorities in recent years, facilitating the application of the model to the Algerian context. The findings derived from the application of this mathematical compartmental model indicate that the basic reproduction number for certain infectious diseases in Algeria (Tuberculosis and COVID-19) is less than one. This observation suggests the potential for disease eradication or effective management through a combination of targeted interventions including vaccination, high-quality treatment, and precise isolation measures.

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Bilal BASTI , , (2024-06-01), Fractional Mathematical Model for Exploring the Influence of Infectious Diseases on Population with Chronic Conditions, Advanced Theory and Simulations, Vol:7, Issue:8, pages:2301285, Wiley-VCH GmbH

In our present work, we thoroughly examine and provide analytical insights into a mathematical models for infectious diseases as COVID-19, employing the Caputo-Katugampola derivative. Numerous stability results are meticulously computed based on well-defined parameters, ensuring compliance with conditions that effectively impede pandemic occurrences. Furthermore, the paper rigorously investigates the critical aspect of the existence and uniqueness of solutions for the SIRD model, leveraging the robust properties inherent in Schauder's and Banach's fixed point theorems. This multifaceted analysis not only enhances our understanding of the intricate dynamics of COVID-19 but also contributes valuable knowledge to the broader field of mathematical epidemiology.

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Bilal BASTI , ,(2023-12-13), Mathematical Modeling and Analysis for Studying the Behavior of Infectious Diseases,Mathematical Modeling for Biology and Health "MMBS-2023",Mohamed Boudiaf University of M'sila

In our present work, we thoroughly examine and provide analytical insights into a mathematical model characterizing the fractional-order SIRD dynamics for COVID-19, employing the Caputo-Katugampola derivative. Numerous stability results are meticulously computed based on well-defined parameters, ensuring compliance with conditions that effectively impede pandemic occurrences. Furthermore, the paper rigorously investigates the critical aspect of the existence and uniqueness of solutions for the SIRD model, leveraging the robust properties inherent in Schauder's and Banach's fixed point theorems. This multifaceted analysis not only enhances our understanding of the intricate dynamics of COVID-19 but also contributes valuable knowledge to the broader field of mathematical epidemiology.

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Bilal BASTI , ,(2023-11-26), Forecast and Analysis on the Spread of COVID-19 with Fractional Operators,International Conference on Contemporary Mathematics and its Applications (ICCMA 2023),Mila University Center, Algeria

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.

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Bilal BASTI , ,(2023-11-20), Well-Posedness of the Multidimensional Nonlinear Free Energy Equation for Modeling Many Physical Phenomena,Statistiques et Analyse Avancées: Domaines d'Interactions et d'Applications (SAADIA 1),l’université de Bejaia, Algeria

In this paper, we examine the existence and uniqueness of solutions under the traveling wave forms for a free boundary Cauchy problem of space-fractional Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics, which describe sound propagation in thermo-viscous elastic terms. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems, while Caputo’s fractional derivative is used as the differential operator. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results.

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Bilal BASTI , , (2023-10-18), Cauchy problem for Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics with fractional operators, Annals of the Alexandru Ioan Cuza University - Mathematics, Vol:69, Issue:2, pages:143-161, Universitatii Al.I.Cuza din Iasi

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, application of Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation. The applicability of our main results is demonstrated through examples and explicit solutions.

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Bilal BASTI , , (2023-09-01), Theoretical Studies on the Existence and Uniqueness of Solutions for a Multidimensional Nonlinear Time and Space-Fractional Reaction-Diffusion/Wave Equation, Memoirs on Differential Equations and Mathematical Physics, Vol:89, Issue:, pages:1-16, Andrea Razmadze Mathematical Institute

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, applying Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation.

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Bilal BASTI , ,(2023-08-26), A hybrid model for a class of multidimensional nonlinear free energy equations,23rd International Pure Mathematics Conference,University of Islamabad - Pakistan

This paper examines the existence and uniqueness of solutions under the traveling wave forms for a free boundary Cauchy problem of space-fractional Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics, which describe sound propagation in thermo-viscous elastic terms. It does so by applying the properties of Banach's fixed point theorem.

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Bilal BASTI , ,(2023-07-04), View analysis of nonlinear acoustic wave equations in terms of viscoelasticity,The Second Online National Conference on Pure and Applied Mathematics,Université Echahid Cheikh Larbi Tebessi– Tebessa, Algeria

This paper discusses and provides some analytical studies for a hybrid mathematical model of COVID-19, which is a SECIRD fractional model that is concerned with the influence of the pandemic on chronically ill people. We compute and derive several stability results based on some parameters that satisfy some conditions that prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SECIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

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Bilal BASTI , ,(2023-06-28), ANALYTICAL STUDIES FOR A HYBRID MATHEMATICAL MODEL OF COVID-19: THE INFLUENCE OF THE PANDEMIC ON CHRONICALLY ILL PEOPLE,2nd Edition of the International Symposium & International Student Workshop on Interdisciplinary Mathematics in the CiTi areas (ISIM & ISWIM),National University of Science and Technology POLITEHNICA Bucharest, Romania

Nonlinear fractional partial differential equations (PDEs) have been used to model many phenomena in various fields, such as mathematics and physics, and the evolution of phenomena in different scientific areas. The property of the fractional derivative operators plays an especially crucial role in applied mathematics and physics. Exact solutions of fractional equations are used to mathematically formulate and, thus, aid in defining the solution of physical and other problems, including functions of several variables such as the propagation of heat or sound, etc. Several mathematical models are used to describe nonlinear acoustic phenomena. For example, in this work, we shall give a fractional model of nonlinear acoustics named the space-fractional Jordan-Moore-Gibson-Thompson (JMGT) equation. This equation results from modeling high-frequency ultrasound waves.

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Bilal BASTI , ,(2023-06-01), Thermodynamical Problem of High-Frequency Ultra Sound Waves Equation with Fractional Operators,International Conference of Young Mathematicians,The Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine

This paper investigates the problem of the existence and uniqueness of one solution under the traveling wave form for a free boundary problem of a space-fractional wave equation with an inverse source term. It does so by applying Banach's fixed point theorem.

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Bilal BASTI , ,(2023-05-14), Effective results concerning new functional solutions of fractional hyperbolic problems with an inverse source term,The first National Applied Mathematics Seminar,Mohamed Khider University of Biskra, Algeria

In this paper, we discuss and provide some analytical studies for a mathematical model of fractional-order SEIRD for COVID-19 in the sense of the Caputo-Katugamp ola derivative. We compute and derive several stability results based on some parameters that satisfy some conditions that prevent the pandemic from occurring. The paper also investigates the problem of the existence and uniqueness of solutions for the SEIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed-point theorem.

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Bilal BASTI , ,(2023-05-13), Application of Fractional Calculus in The Modeling of Biological Phenomena and Infectious Diseases,Second National Conference on Applied Mathematics and Didactics,Ecole Normale Supérieure Assia Djebar – Constantine, Algeria

This paper offers a thorough discussion and study of the existence and uniqueness of solutions proposed for a class of new systems of n-nonlinear fractional differential equations and their main properties using the fractional derivative of Katugampola with n integral conditions. Schauder’s fixed point theorem, the Banach contraction principle, and Leray-Schauder type nonlinear alternative are applied to attain the desired goal. In order to exhibit the usefulness of our main results, several examples are also presented in the paper.

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Bilal BASTI , , (2023-01-10), Existence Study of Solutions for a System of n-Nonlinear Fractional Differential Equations with Integral Conditions, Journal of Mathematical Physics, Analysis, Geometry, Vol:18, Issue:3, pages:350-367, ILTPE-B. Verkin Institute for Low Temperature Physics and Engineering

This paper examines the existence and uniqueness of solutions under the traveling wave forms for a free boundary Cauchy problem of space-fractional Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics, which describe sound propagation in thermo-viscous elastic terms. It does so by applying the properties of Banach's fixed point theorem.

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Bilal BASTI , ,(2022-12-18), Thermo-viscous elastic free boundary problem of fractional PDEs of nonlinear acoustics,THE SECOND NATIONAL CONFERENCE ON PURE AND APPLIED MATHEMATICS (NCPAM2022),Amar Telidji University of Laghouat, Algeria

The fractional wave equation of higher order is presented as a generalization of the higher-order wave equation when arbitrary fractional-order derivatives are involved. This paper investigates the problem of existence and uniqueness of solutions under the traveling wave forms for a free boundary problem of higher-order space-fractional wave equations. It does so by applying the properties of Schauder's and Banach's fixed point theorems.

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Bilal BASTI , , (2022-09-27), Existence Of Traveling Wave Solutions For A Free Boundary Problem Of Higher-Order Space-Fractional Wave Equations, Applied Mathematics E - Notes, Vol:22, Issue:, pages:427-436, Tsinghua University

This paper particularly addresses and discusses some analytical studies on the existence and uniqueness of global or blow-up solutions under the traveling profile forms for a free boundary problem of two-dimensional diffusion equations of moving fractional order. It does so by applying the properties of Schauder's and Banach's fixed-point theorems. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results.

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Bilal BASTI , , (2022-03-10), Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order, Advances in the Theory of Nonlinear Analysis and its Application, Vol:6, Issue:3, pages:287-299, DergiPark

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

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Bilal BASTI , , (2021-08-04), Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives, Symmetry, Vol:13, Issue:8, pages:1431, Multidisciplinary Digital Publishing Institute (MDPI)

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

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Bilal BASTI , , (2021-05-29), Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions, Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Vol:20, Issue:, pages:43-56, Sciendo, De Gruyter Brill company

This paper investigates the problem of existence and uniqueness of positive solutions under the general self-similar form of the degenerate parabolic partial differential equation which is known as "nonlinear diffusion equation not in divergence form". By applying the properties of Banach's fixed point theorems, we establish several results on the existence and uniqueness of the general form of self-similar solutions of this equation.

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Bilal BASTI , , (2020-09-05), Global Existence And Blow-Up Of Generalized Self-Similar Solutions To Nonlinear Degenerate Diffusion Equation Not In Divergence Form, Applied Mathematics E - Notes, Vol:20, Issue:, pages:367-387, Tsinghua University

This work studies the existence and uniqueness of solutions for a class of nonlinear fractional differential equations via the Katugampola fractional derivatives with an integral condition. The arguments for the study are based up on the Banach contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type.

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Bilal BASTI , , (2020-04-16), Existence results for nonlinear Katugampola fractional differential equations with an integral condition, Acta Mathematica Universitatis Comenianae, Vol:89, Issue:2, pages:243-260, Univerzita Komenskeho

This paper investigates the problem of existence and uniqueness of solutions under the self-similar forms to the space-fractional heat equation. By applying the properties of Banach's fixed point theorems, Schauder's fixed point theorem and the nonlinear alternative of Leray-Schauder type, we establish several results on the existence and uniqueness of self-similar solutions to this equation.

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Bilal BASTI , , (2020-02-07), Existence Results of Self-similar Solutions to The Caputo-type’s Space-fractional Heat Equation, Surveys in Mathematics and its Applications, Vol:15, Issue:, pages:153-168, University Constantin Brancusi of Targu-Jiu

The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For application purposes, some examples are provided to demonstrate the usefulness of our main results.

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Bilal BASTI , , (2019-07-31), Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations, Journal of Mathematics and Applications, Vol:42, Issue:, pages:35-61, Rzeszów University of Technology.

In this thesis, we discuss several existence and uniqueness results of generalized self-similar solutions for some nonlinear partial differential equations of fractional order of Katugampola type, with boundary value, initial value, or with integral conditions in Banach space, we use the Banach contraction principle, Schauder and Guo-Krasnosel'skii fixed point theorems, and the technique of the nonlinear alternative of Leray-Schauder type.

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BilalBASTI , ,(2019-05-04); Existence et unicité de solutions auto-similaires générales pour certaines équations fractionnaires non-linéaires,Mohamed Boudiaf University of M'sila,

This work studies the existence and uniqueness of solutions for a class of nonlinear implicit fractional differential equations via the Katugampola fractional derivatives with an initial condition. The arguments for the study are based upon the Banach contraction principle, Schauder's fixed point theorem, and the nonlinear alternative of Leray-Schauder type.

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Bilal BASTI , , (2019-01-01), Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola Derivative, Applied Mathematics E - Notes, Vol:19, Issue:, pages:397-412, Tsinghua University