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

Abstract

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.

Keywords

• Hybrid boundary value problem
• Banach space
• Coupled fixed point theorem
• Caputo's fractional derivative.