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

Volume 12, Issue 12, pp 791--798
Publication Date: July 07, 2019 Submission Date: April 02, 2019 Revision Date: May 31, 2019 Accteptance Date: June 16, 2019
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### Authors

Ahmed Salem - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia. Faris Alzahrani - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia. Lamya Almaghamsi - 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.

### Abstract

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.

### Keywords

• Fractional Langevin equations
• fixed point theorem
• existence and uniqueness

•  26A33
•  34A08
•  34A12
•  34B15

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