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

Volume 12, Issue 12, pp 791--798 http://dx.doi.org/10.22436/jnsa.012.12.02 Publication Date: July 07, 2019       Article History

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.


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