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Existence of mild solutions to Hilfer fractional evolution equations in Banach space

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arxiv 1812.02213 v1 pith:W5BSMFG7 submitted 2018-12-05 math.CA

J. Vanterler da C. Sousa This is my paper · ORCID
classification math.CA
keywords banachevolutionexistencefractionalhilfermildsolutionsspace
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abstract

In this paper, we investigate the existence of mild solutions to Hilfer fractional equation of semi-linear evolution with non-instantaneous impulses, using the concepts of equicontinuous $C_{0}$-semigroup and Kuratowski measure of non-compactness in Banach space $\Omega$.

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  1. Ulam-Hyers stabilities of mild solutions of the fractional nonlinear abstract Cauchy problem

    math.CA 2019-08 conditional novelty 4.0 of 10

    The authors prove Ulam-Hyers and Ulam-Hyers-Rassias stability for mild solutions of a Hilfer fractional abstract Cauchy problem on [0,T] and [0,∞) using the Banach fixed point theorem.

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