SAAD Abdelkebir

MAKHLOUF Nour elhouda

Exact and approximate solutions for deformable fractional differential equations

MAKHLOUF Nour elhouda

Exact and approximate solutions for deformable fractional differential equations

SALHI Djihad

Solutions semi-analytiques pour les équations aux dérivées conformable et local fractionnaires

AICHE Ilham

Existence and uniqueness of the solutions for a nonlinear time-conformable fractional reaction-diffusion equations with delay

ATHMANI Fatima

Étude d’un problème inverse pour l’équation télégraphique linéaire

BOUAZIZ Khalisa

Résolution analytique et numérique de l’équation de télégraphe conformable fractionnaire

NEDJAI Naziha

Étude une classe des équations intégro-différentielles de type Volterra d’ordre fractionnaire avec condition a la limite non locale

SAOUDI Dhiya Eddine Aymen

Méthode de transformation différentielle réduite pour la résolution d’équations aux dérivées partielles fractionnaires

Bounif mey manel

Problème d’évolution pour une équation de diffusion-onde fractionnaire définie dans un domaine borné

In this paper, a numerical approach is proposed for solving the one-dimensional space-time-fractional telegraph equations with variable coefficients and Robin’s boundary conditions. The fractional derivatives are described in the conformable sense. Based on the Legendre collocation method, our problem is reduced to a linear system of second order differential equations and the Generalized-α method is applied to solve this system. With five examples, we present a comparative study between our algorithm and some numerical methods available in the literature. This algorithm gives an excellent approximation with a small number of collocation points.

Citation

Saad ABDELKEBIR , BRAHIM Nouiri , , (2024-09-01), A numerical approach of the space-time-fractional telegraph equations with variable coefficients, Palestine Journal of Mathematics, Vol:13, Issue:3, pages:20, Brahim NOUIRI and Saad ABDELKEBIR

In this article, we explain the existence and the uniqueness of the solutions associated with the non-linear fractional integro-differential equation of Volterra for the fractional derivative of Caputo of values at local conditional limits. This work is mainly based on the application of the theory of fixed points in the Banach space. This work will be supported by an example at the end .

Citation

Saad ABDELKEBIR , , (2024-09-01), EXISTENCE AND UNIQUENESS RESULTS FOR A NONLINEAR FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATION WITH NON-LOCAL BOUNDARY CONDITIONS, Palestine Journal of Mathematics, Vol:13, Issue:3, pages:08, Saad ABDELKEBIR

In this talk, we study the existence and the uniqueness of the solutions of the nonlinear time- conformable fractional reaction-diffusion equations with delay. This equation is defined by a fractional deriva- tive in terms of time, called the Conformable derivative (see [1],[2]). Using Lebesgue dominated convergence theorem [5], Leray–Schauder fixed point theorem and Banach contraction mapping theorem [3],[4]. We obtain some sufficient conditions for the existence of the solutions of the above conformable fractional order partial differential equations. Keywords: 35R11, 35K57, 33E12. 2020 Mathematics Subject Classification Numbers: Conformable derivative ,Reaction-diffusion equations, Fixed point theorems.

Citation

Saad ABDELKEBIR , ,(2023-07-05), Existence and uniqueness of the solutions for a nonlinear time-conformable fractional reaction-diffusion equations with delay,7th International Conference of Mathematical Sciences (ICMS 2023),Maltepe University, Istanbul, Turkey

In this paper, we present an analytical method to solve a time-conformable fractional telegraph equation with three boundary conditions namely, Dirichlet, Neumann and Robin. This method based on Fourier method and conformable fractional calculus properties. We give three examples to validate this method.

Citation

Saad ABDELKEBIR , Saad ABDELKEBIR , BRAHIM Nouiri , , (2023), Analytical method for solving a time-conformable fractional telegraph equation, Filomat, Vol:37, Issue:9, pages:1-14, The Faculty of Sciences and Mathematics, University of Nis. Ministry of Education, Science and Technological Develpoment, Republic of Serbia.

In this paper, we present an analytical method to solve a time-conformable fractional telegraph equation with three boundary conditions namely, Dirichlet, Neumann and Robin. This method based on Fourier method and conformable fractional calculus properties. We give three examples to validate this method.

Citation

Saad ABDELKEBIR , Saad ABDELKEBIR , BRAHIM Nouiri , , (2023), Analytical method for solving a time-conformable fractional telegraph equation, Filomat, Vol:37, Issue:9, pages:1-14, The Faculty of Sciences and Mathematics, University of Nis. Ministry of Education, Science and Technological Develpoment, Republic of Serbia.

In this paper, we present an analytical method to solve a time-conformable fractional telegraph equation with three boundary conditions namely, Dirichlet, Neumann and Robin. This method based on Fourier method and conformable fractional calculus properties. We give three examples to validate this method.

Citation

Saad ABDELKEBIR , BRAHIM Nouiri , , (2022-10-23), Analytical method for solving a time-conformable fractional telegraph equation, Filomat, Vol:37, Issue:9, pages:13, Published by Faculty of Sciences and Mathematics, University of Nis, Serbia

In this work, a new algorithm is proposed for solving the time-space-fractional linear telegraph equations with variable coefficients and Robin boundary conditions. The fractional derivatives are described in the conformable sense. This algorithm is based on shifted Legendre polynomials of the first kind and α-Generalized method. The time-space fractional telegraph equations is reduced to a linear system of second order differential equations and the α-Generalized method is applied to solve this system. Finally, some numerical examples are presented to confirm the reliability and effectiveness of this algorithm. Keywords: Conformable fractional calculus, α-Generalized method, Legendre polynomials, Time-space-fractional telegraph equation with variable coefficients. 2020 Mathematics Subject Classification Numbers: 35R11, 26A33, 33C45.

Citation

Saad ABDELKEBIR , ,(2022-07-20), A new algorithm for solving the time-space-fractional linear telegraph equations with variable coefficients,6th International Conference of Mathematical Sciences (ICMS 2022),Maltepe University, İstanbul Turkey

In this presentation, we present an algorithm to find the approximate solutions of the fractional heat equation conformable with a source using the Logendre polynomials and Euler's method.

Citation

Saad ABDELKEBIR , ,(2022), Numerical method for solving the conformable time-space fractional convective heat equation with a source using shifted Legendre collocation method”,6th International Conference of Mathematical Sciences (ICMS 2022),Turkey

In this presentation, we present new method to find the approximate solutions or semi-analytical solutions of the fractional differential equation conformable using the Reduced Differential Transformation Method (RDTM) .

Citation

Saad ABDELKEBIR , ,(2021), Approach Solution For Fractional Differential Equation By Conformable Reduced Differential Transformation Method,1st International Conference on Pure and Applied Mathematics,Univ Ouargla, Algeria

In this presentation, we have found the exact solutions of the conformable fractional Trocimi equation using the Fourier and Laplace transforms.

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Saad ABDELKEBIR , ,(2020), Analytical Conformable Solution for Time-Fractional Generalized Tricomi Equation by the Method of Separation Variables,The First Online Conference on Modern Fractional Calculus and Its Applications,Turkey

In this paper, the Fourier method is effectively implemented for solving a conformable fractional telegraph equation. We discuss and derive the analytical solution of the conformable fractional telegraph equation with threekinds of nonhomogeneous boundary conditions, namely, Dirichlet.

Citation

Saad ABDELKEBIR , ,(2019), Analytical solution for the conformable fractional telegraph equation by Fourier method,icms'2019,Turkey

In this paper, the Fourier method is effectively implemented for solving a conformable fractional telegraph equation. We discuss and derive the analytical solution of the conformable fractional telegraph equation with nonhomogeneous Dirichlet boundary condition.

Citation

Saad ABDELKEBIR , BRAHIM Nouiri , ,(2019), ANALYTICAL SOLUTION FOR THE CONFORMABLE FRACTIONAL TELEGRAPH EQUATION BY FOURIER METHOD,Third International Conference of Mathematical Sciences (ICMS 2019),Maltepe University, Istanbul, Turkey

Dans ce travail, nous avons présenté la méthode de transformation différentielle réduite basée sur la technique de développement en série de puissance pour résoudre analytique- ment des équations aux dérivées partielles fractionnaires avec des conditions initiales appropriées. L'utilisation de cette méthode il est possible de trouver une solution exacte ou une solution approchée fermée. La précision, l’efficacité et la convergence de cette méthode sont démontrées à travers des exemples numériques.

Citation

Saad ABDELKEBIR , BRAHIM Nouiri , ,(2018), Méthode de transformation différentielle réduite pour des équations aux dérivées partielles fractionnaires,Workshops on Pure and Applied Mathematics,M'sila, Algeria