Existence results for a coupled system of nonlinear fractional differential equations with boundary value problems on an unbounded domain

This paper deals with the existence results for solutions of coupled system of nonlinear fractional differential equations with boundary value problems on an unbounded domain. Also, we give an illustrative example in order to indicate the validity of our assumptions

Existence of positive solutions to a coupled system of fractional hybrid differential equations

where Dα is the Caputo’s fractional derivative of order α ,1 0 and the functions f : j × R × R → R , f (0,0) = 0 and g : j × R× R → R 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. Finally, our results are illustrated by providing a counter example