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Dynamics and stability of pantograph equations via Hilfer fractional derivative. (English) Zbl 1357.34020

Summary: In this paper we analyse existence, uniquness, Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for pantograph equation with Hilfer fractional derivative. The existence result is obtained by using the Scheafer’s fixed point theorem.

MSC:

34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
45G05 Singular nonlinear integral equations
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