YACINE Arioua

Chikouche Imane

Existence and Uniqueness of Solutions for Nonlinear Ψ-Fractional Differential Equations and their System

Messad Youssef

Some Results on the Cauchy Type Problems of Fractional q-Differential Equations

Ouagueni Nora

Etude d’existence et d’unicité de solutions pour certaines classes d’EDPs fractionnaires

بوشامة كوثر

Méthodes numériques pour la résolution des équations différentielles fractionnaires

بكاي محمد

Solution for a Fractional Boundary Value Problems on the Infinite Interval

HOUD Kheirddine

Problèmes inverses pour une equation aux dérivées partielles en temps avec dérivée fractionnaire généralise

Maria Titraoui

Etude d'existencre et d'unicité de certaines classes d'équations différentielles fractionnaires

Tabeni Mohammed

Boundary value problem for nonlinear Caputo-katugampola fractional differential equations

Bouguerra Marwa

Boundary value problem for nonlinear q-symmetric fractional differential equations

Basti Bilal

Existence et unicité de solutions auto-similaires générales pour certaines équations fractionnaires non-linéaires

Achour Hayat

Résultas d'existence de preblème aux limites d'equations différentielles fractionnaires non linéaires

Touama Randa , Khodja Nourelhoda

Eléments de calcul fractionnaire - théorie et application

Lakehal Rachid

Équation différentielle fractionnaire - résultats d’existence et d’unicité

Ouagueni Noura

L'équation des milieux poreux fractionnaire

Faide Nourelhoda

Problème de Cauchy pour l'équation de diffusion fractionnaire

Dilmi Mehamed

Solution auto similaire pour un système de type milieu poreux

In this paper, we shall study the existence and uniqueness of solutions called "traveling profiles solutions" to the porous medium equation in one dimension. By these solutions, we generalize the results obtained by Gilding and Peletier who proved the existence of self similar solutions of type I, II and III to the same equation. The principal idea of our work is to convert the porous media equation in to an equivalent nonlinear differential equation, and to prove the existence and uniqueness of these new solutions under certain conditions.

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YACINE Arioua , Noureddine BENHAMIDOUCHE , , (2023-12-21), Existence of Traveling Profiles Solutions to Porous Medium Equation, Journal officiel Mathematics and Application, Vol:46, Issue:1, pages:149-162, Publishing House of Rzeszów University of Technology P.O. Box 85, 35-959 Rzeszów, Poland

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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YACINE Arioua , Basti Bilal, , (2023-05-16), 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, National Academy of Sciences of Ukraine B.Verkin Institute for Low Temperature Physics and Engineering.

In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity vari- able η, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed point theorems (i.e. Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).

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YACINE Arioua , Noureddine BENHAMIDOUCHE , Ouagueni Nora, , (2023-04-03), Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative, Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Vol:22, Issue:1, pages:49-74, Sciendo

This paper is devoted to the existence and uniqueness of solution to a class of Hadamard fractional differential equation under fractional Sobolev spaces. A novel form of fractional Sobolev space via Hadamard fractional operator is well proposed and related properties are also proved. Furthermore, a variational formulation of considered system is established and thereby the Lax-Milgram theorem is also employed to demonstrate the existence and uniqueness.

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YACINE Arioua , Mohamedourabah BENMEDDOUR , ABDERACHID Saadi , , (2023-03-13), Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative, Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES, Vol:18, Issue:1, pages:61-83, Bulletin, Institute of Mathematics, Academia Sinica

In this paper, we provide an accurate numerical solution for space-time fractional linear diffusion equation involving the fractinal Caputo-Hadamard derivative. To do so, we have used a finite difference method. The Convergence and stability of the given finite difference scheme are studied using the mathematical induction technique. Moreover, Numerical examples are given to demonstrate the effectiveness of our results.

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KAOUTHER Bouchama , YACINE Arioua , Abdelkrim MERZOUGUI , , (2023), Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative, International Journal of Applied and Computational Mathematics, Vol:9, Issue:4, pages:52, Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

In this paper, we have discussed a special type of nonlinear boundary value problems (BVPs) which involves both the right-sided Caputo-Katugampola (CK) and the left-sided Katugampola fractional derivatives (FDs). Based on some new techniques and some properties of the Mittag-Le er functions, we have introduced a formula of the solution for the aforementioned problem. To study the existence and uniqueness results of the solution for this problem, we have applied some known xed point theorems (i.e., Banachs contraction principle, Schauders xed point theorem, nonlinear alternative of Leray-Schauder type and Schaefers xed point theorem). We have also studied the Ulam-Hyers stability of this problem. To illustrate the theoretical results in this work, we have given two examples.

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YACINE Arioua , Nora Ouagueni, , (2022), Existence And Uniqueness Of Solution For A Mixed-Type Fractional Di¤erential Equation And Ulam-Hyers Stability, Applied Mathematics E-not, Vol:22, Issue:1, pages:476-495, Tsing Hua University Hsinchu, TAIWAN

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 frac￾tional 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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YACINE Arioua , Bilal Basti, , (2022), 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, National Academy of Sciences of Ukraine, B.Verkin Institute for Low Temperature Physics and Engineering.

Existence and uniqueness results of self-similar solutions of the space-fractional diffusion equation

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YACINE Arioua , Nora ouagueni, ,(2022), Existence and uniqueness results of self-similar solutions of the space-fractional diffusion equation,3rd International Conference on Applied Engineering and Natural Sciences,Konya/Turkey

The main objective of this paper is to find accurate solutions for linear fractional differential equations involving the fractional Caputo-Hadamard derivative of order α > 0. Therefore, to achieve this objective, a new method called the Finite Fractional Difference Method (FFDM) is employed to find the numerical solution. As such, the convergence and stability of the numerical scheme is discussed and illustrated by solving two linear fractional differential equation problems of order 0 < α<=1 to show the validity of our method.

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KAOUTHER Bouchama , Abdelkrim MERZOUGUI , YACINE Arioua , ADMIN Admin , , (2022), Numerical solutions for linear fractional differential equation with dependence on the Caputo-Hadamard derivative using finite difference method, Palestine Journal of Mathematics, Vol:11, Issue:, pages:28-36, Nouressadat Touafek

In this paper, a numerical approximation solution of a space-time fractional diffusion equation (FDE), involving Caputo-Katugampola fractional derivative is considered. Stability and convergence of the proposed scheme are discussed using mathematical induction. Finally, the proposed method is validated through numerical simulation results of different examples.

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KAOUTHER Bouchama , YACINE Arioua , Abdelkrim MERZOUGUI , , (2022), The numerical solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative, Numerical Algebra, Control and Optimization, Vol:12, Issue:3, pages:621-636, Bulent Karasozen

In this paper, we focus on the boundary value problem (BVP) for a coupled system of nonlinear fractional differential equations (SFDEs) involving the Erdélyi-Kober derivatives on an innite interval. First, we dene the integral solution of the BVP for Erdélyi-Kober (SFDEs). Then, by using the Banach contraction principle and the Leray-Schauder nonlinear alternative xed point theorem in a special Banach space, existence and uniqueness theorems of the given problem are demonstrated, respectively. Finally, several indispensable examples are presented to illustrate the usefulness of our main results.

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YACINE Arioua , Maria Titraoui, , (2021), Boundary Value Problem For A Coupled System Of Nonlinear Fractional Differential Equations Involving Erdélyi-Kober Derivative, Applied mathematics E-Notes, Vol:21, Issue:, pages:291-306, China

In this paper, we establish sufficient conditions for the existence of bounded solution for a class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi–Kober differential operator on unbounded domain. Our results are based on a fixed point theorem of Schauder combined with the diagonalization argument method in a special Banach space. To that end, an example is presented to illustrate the usefulness of our main results.

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YACINE Arioua , Maria Titraoui, , (2021), Boundary value problem for nonlinear fractional differential equations involving Erd´elyi–Kober derivative on unbounded domain, Annals of the University of Craiova, Mathematics and Computer Science Series, Vol:48, Issue:1, pages:18-31, University of Craiova

This paper is devoted to establishing vital criteria of existence and uniqueness for a class of nonlinear Katugampola fractional differential equations (KFDEs) with p-Laplacian operator subjecting to mixed boundary conditions. The reasoning is inspired by diverse classical f ixed point theory, such as the Guo-Krasnosel’skii type fixed point principle and Banach contraction theorem. Additionally, several expressive examples are afforded to show the effectiveness of our theoretical results.

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YACINE Arioua , Li Ma, , (2021), ON CRITERIA OF EXISTENCE FOR NONLINEAR KATUGAMPOLA FRACTIONAL DIFFERENTIAL EQUATIONS WITH p–LAPLACIAN OPERATOR, Fractional Differential Calculus, Vol:11, Issue:1, pages:55-68, www.ele-math.com

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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YACINE Arioua , Benhamidouche NourEddine , Basti Bilal, , (2020), Existence results for nonlinear Katugampola fractional differential equations with an integral condition, Acta Mathematica Universitatis Comenianae, Vol:89, Issue:2, pages:243-260, Comenius University, 842 48 Bratislava, Slovak Republic

In this paper, we investigate the existence and uniqueness of solutions to a class of boundary value problem of nonlinear Caputo type Erdély Kober fractional differential equations

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YACINE Arioua , , (2020), UNBOUNDED SOLUTION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR CAPUTO-TYPE ERDELYI KOBER FRACTIONAL DIFFERENTIAL EQUATION ON THE HALF-LINE, Dynamic of Continuous Discrete and Impulsive Systems Serie A, Vol:28, Issue:1, pages:51-76, Watam Press

The objective of this present work is to study various approaches to the numerical solution of fractional partial differential equations (FPDEs) of the Caputo-Katugampola type. Among the intriguing methods explored in our study, we emphasize the Adomian Decomposition Method (ADM), the Homotopy Perturbation Method (HPM), and the Iterative Decomposition Method (IDM).

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KAOUTHER Bouchama , Abdelkrim MERZOUGUI , YACINE Arioua , ,(2019-11-21), Fractional Differential Equations of Caputo- Katugampola Type and numerical Solutions,RAMA 11,Sidi Bel Abbès

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, Schauders fixed point theorem and the nonlinear alternative of Leray-Schauder type

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YACINE Arioua , Noureddine BENHAMIDOUCHE , Basti bilal, , (2019), Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola, Applied Mathematics E-Notes, Vol:19, Issue:19, pages:397-412, Tsing Hua University Hsinchu, TAIWAN

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 xed point theo- rems. For applications purposes, some examples are provided to demon- strate the usefulness of our main results.

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YACINE Arioua , Noureddine BENHAMIDOUCHE , Basti Bilal, , (2019), Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations, Journal of Mathematics and Applications, Vol:42, Issue:42, pages:35-61, Publishing House of Rzeszow University of Technology, Poland

The aim of this work is to study the initial value problem of a coupled system of nonlinear fractional differential equations with Katugampola derivative. Some new existence and uniqueness results of solutions for the given problems are obtained by using the Banach contraction principle, Schauder’s and nonlinear alternative Leray–Schauder fixed point theorems. Several examples are presented to illustrate the usefulness of our main results

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YACINE Arioua , , (2019), Initial Value Problem for a Coupled System of Katugampola-Type Fractional Differential Equations, Advances in Dynamical Systems and Applications, Vol:14, Issue:1, pages:29–47, Research India Publications

In this paper, we introduce a new class of boundary value problem for nonlinear fractional dierential equations involving the Erdélyi- -Kober differential operator on an innite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii xed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main results

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YACINE Arioua , Titraoui Maria, , (2019), New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative, Communications in Mathematics, Vol:27, Issue:, pages:113-141, University of Ostrava, Czech Republic

The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii’s fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained

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YACINE Arioua , Noureddine BENHAMIDOUCHE , , (2017), BOUNDARY VALUE PROBLEM FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS, Surveys in Mathematics and its Applications, Vol:12, Issue:12, pages:103-115, Bucharest University, Romania

Existence results for nonlinear fractional differential equations with Caputo-Hadamard derivative

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YACINE Arioua , ,(2017), Existence results for nonlinear fractional differential equations with Caputo-Hadamard derivative,Mathématiques en images, MI’2017,Université de M'sila

Boundary value problem for Caputo-Katugampola fractional differential equations

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YACINE Arioua , ,(2017), Boundary value problem for Caputo-Katugampola fractional differential equations,Journeés doctoral JDO2017,Université de M'sila

In this paper, we propose a general self similar solutions to the porous medium. We also discuss their existence for some initial data in one dimension. We find for some particular cases an explicit exact solutions. these solutions are called "travelling pro…le solutions".

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YACINE Arioua , ,(2016), Existence of general self similar solution to porous medium equation,International Arab Conference on Mathematics and Computations (2016),,Zarqa University, Jordan

Traveling profiles solutions to heat equation with a power-law nonlinearity

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YACINE Arioua , ,(2016), Traveling profiles solutions to heat equation with a power-law nonlinearity,Congrès des Mathématiciens Algériens CMA'2016,Université de Batna

Solutions de l'équation des milieux poreux par la méthode des profiles mobiles

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YACINE Arioua , ,(2012), Solutions de l'équation des milieux poreux par la méthode des profiles mobiles,Congrès des Mathématiciens Algériens CMA'2012,Université de Annaba

We propose in this paper a new approach to construct exact solutions of nonlinear PDEs. The method used is called ”the travelling profiles method”. The travelling profiles method enables us to obtain many exact solutions to large classes of nonlinear PDEs

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YACINE Arioua , Noureddine BENHAMIDOUCHE , , (2009), New Method for Constructing Exact Solutions to Nonlinear PDEs, International Journal of Nonlinear Science, Vol:7, Issue:4, pages:395-398, World Academic Press, World Academic Union, England, UK

New exact solutions to porous medium equation with traveling wavelets in one dimension

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YACINE Arioua , ,(2007), New exact solutions to porous medium equation with traveling wavelets in one dimension,2ièm colloque internationale sur l'analyse non linéaire et applications (ANL'07),Université de Sétif

Etude de l'équation de Fujita par la méthode des Ondelettes mobiles

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YACINE Arioua , ,(2006), Etude de l'équation de Fujita par la méthode des Ondelettes mobiles,Rencontre internationale d'analyse mathématique et ses applications (RAMA V),Université de M'sila

Financial markets modeling

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YACINE Arioua , ,(2005), Participation in the CIMPA-UNSA-UNESCO school,Financial markets modeling,University of Irbid, Jordan