Matrix Science Mathematic (MSMK)

ABSTRACT

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

Journal: Matrix Science Mathematic (MSMK)
Author: Ghulam Hussain, Rahmat Ali Khan and Muhammad Iqbal

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2018.09.12

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 Dα 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.