University of TabrizComputational Methods for Differential Equations2345-39821220131001Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations120134597ENHosseinNorooziShahrekord UniversityAlirezaAnsariShahrekord UniversityJournal Article20140106In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation<br />$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$<br />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.https://cmde.tabrizu.ac.ir/article_597_aec82c22b058d25675f6cd533c9fac23.pdf