Hossein Noroozi - Shahrekord University
Alireza Ansari - Shahrekord University

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equationint_{۰}^{۱}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function g, under the generalized Lipschitz and Caratheodory conditions.

Fractional hybrid differential equations, Distributed order, Extremal solutions, Banach algebra