A Study on Impulsive Hilfer Fractional Evolution Equations with Nonlocal Conditions

A Study on Impulsive Hilfer Fractional Evolution Equations with Nonlocal Conditions AbstractIn this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining measure of noncompactness with the fixed-point methods, we obtain the existence results of mild solutions with two new characteristic solution operators. The results we obtained are new and more general to known results. At last, an example is provided to illustrate the results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Nonlinear Sciences and Numerical Simulation de Gruyter

A Study on Impulsive Hilfer Fractional Evolution Equations with Nonlocal Conditions

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Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
2191-0294
eISSN
2191-0294
DOI
10.1515/ijnsns-2019-0015
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining measure of noncompactness with the fixed-point methods, we obtain the existence results of mild solutions with two new characteristic solution operators. The results we obtained are new and more general to known results. At last, an example is provided to illustrate the results.

Journal

International Journal of Nonlinear Sciences and Numerical Simulationde Gruyter

Published: Apr 26, 2020

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