Eur. Phys. J. Special Topics 226, 3577–3590 (2017)
https://doi.org/10.1140/epjst/e2018-00082-0

Regular Article

On fractional Langevin differential equations with anti-periodic boundary conditions

¹ School of Mathematical Science, University of Science and Technology of China, Hefei 230039, P.R. China
² Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
³ School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, P.R. China

^a e-mail: jalzabut@psu.edu.sa

Received: 28 September 2017
Published online: 25 July 2018

Abstract

In this paper, we provide existence criteria for the solutions of p-Laplacian fractional Langevin differential equations with anti-periodic boundary conditions. The Caputo fractional as well as Caputo q-fractional operators are used to address the derivatives. The main results are verified by the help of Leray–Schaefer’s fixed point theorem. We construct an example to illustrate the feasibility of the main theorems. Our results are new and provide extensions to some known theorems in the literature.