Eur. Phys. J. Special Topics 226, 3411–3425 (2017)
https://doi.org/10.1140/epjst/e2018-00030-6

Regular Article

Existence results of fractional differential equations with Riesz–Caputo derivative

¹ College of Mathematics and Finance, Xiangnan University, Chenzhou 423000, P.R. China
² Department of Mathematics and Computer Sciences, Cankaya University, 06530 Balgat, Ankara, Turkey
³ Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P.R. China
⁴ Institute of Applied Nonlinear Science, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, P.R. China

^a e-mail: dumitru@cankaya.edu.tr

Received: 9 June 2017
Received in final form: 2 December 2017
Published online: 25 July 2018

Abstract

This paper is concerned with a class of boundary value problems for fractional differential equations with the Riesz–Caputo derivative, which holds two-sided nonlocal effects. By means of a new fractional Gronwall inequalities and some fixed point theorems, we obtained some existence results of solutions. Three examples are given to illustrate the results.