A coupled fixed point theorem and application to fractional hybrid differential problems

Abstract

This paper is devoted to the study of the existence of solution to the following system of fractional hybrid differential equations: (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) where (Formula presented.) is the R-L fractional derivative of order α, (Formula presented.) , (Formula presented.) , and the functions (Formula presented.) , (Formula presented.) and (Formula presented.) satisfy certain conditions. The proof of the existence theorem is based on a coupled fixed point theorem of Krasnoselskii type, which extends a fixed point theorem of Burton (Appl. Math. Lett. 11:85-88, 1998). Finally, our results are illustrated by a concrete example.