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Existence results for the distributed order fractional hybrid differential equations. (English) Zbl 1261.34010
Summary: We introduce the distributed-order fractional hybrid differential equations involving the Riemann-Liouville differential operator of order \(0 < q < 1\) with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved via a fixed point theorem in the Banach algebras under mixed Lipschitz and Carathéodory conditions.
34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
47N20 Applications of operator theory to differential and integral equations
Full Text: DOI
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