%0 Journal Article
%T Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Noroozi, Hossein
%A Ansari, Alireza
%D 2013
%\ 10/01/2013
%V 1
%N 2
%P 120-134
%! Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations
%K Fractional hybrid differential equations
%K Distributed order
%K Extremal solutions
%K Banach algebra
%R
%X In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$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.
%U https://cmde.tabrizu.ac.ir/article_597_aec82c22b058d25675f6cd533c9fac23.pdf