extremal positive solutions for the distributed order fractional hybrid differential equations
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abstract
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.
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Journal title:
computational methods for differential equationsجلد ۱، شماره ۲، صفحات ۱۲۰-۱۳۴
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