Existence of Positive Solutions to a Coupled System of Fractional Hybrid Differential Equations

Abstract

In this article, we investigate existence and uniqueness of positive solution to coupled system of Caputo's boundary value problem for fractional order differential equations of the form where D α is the Caputo's fractional derivative of order α ,1<α ≤ 2 , j = [0,T ],T > 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.