Title: Solvability of coupled systems of hybrid fractional differential equations and inclusions

Authors: Nana Jin; Shurong Sun

Addresses: School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China ' School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Abstract: In this paper, we investigate the boundary value problems of the coupled systems of hybrid fractional differential equations and inclusions with coupled boundary conditions involving Caputo fractional derivative. By means of Leary-Schauder alternative and Bohnenblust-Karlin fixed point theorem, some results concerning the existence of solutions are obtained. At the same time, we also give the relationship between solutions and upper and lower solutions. Finally, examples are presented to illustrate our main results.

Keywords: upper and lower solutions; coupled system; hybrid fractional differential equations and inclusions; existence of solutions.

DOI: 10.1504/IJDSDE.2018.096210

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.4, pp.296 - 312

Received: 06 May 2017
Accepted: 04 Oct 2017
Published online: 19 Nov 2018 *

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