Langevin equation involving one fractional order with three-point boundary conditions

Salem, Ahmed ¹ ; Alzahrani, Faris ¹ ; Almaghamsi, Lamya ²

¹ Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia
² Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia;Department of Mathematics, University of Jeddah, 41510, Saudi Arabia

Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 12, p. 791-798.

Résumé

In this paper, we investigate a class of nonlinear Langevin equation involving one fractional order $\alpha\in(0, 1]$ with three-point boundary conditions. By the Banach contraction principle and Krasnoselskii's fixed point theorem, the existence and uniqueness results of solutions are obtained. Two examples are given to show the applicability of our main results.

Détail

DOI : 10.22436/jnsa.012.12.02

Classification : 26A33, 34A08, 34A12, 34B15
Keywords: Fractional Langevin equations, fixed point theorem, existence and uniqueness

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