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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 68, Issue 6

Issues

Cauchy problems involving a Hadamard-type fractional derivative

Rafał Kamocki
Published Online: 2018-11-20 | DOI: https://doi.org/10.1515/ms-2017-0186

Abstract

In this paper, we investigate some Cauchy problems involving a left-sided Hadamard-type fractional derivative. A theorem on the existence of a unique solution to a nonlinear problem is proved. The main result is obtained using a fixed point theorem due to Banach, as well as the Bielecki norm. A Cauchy formula for the solution of the linear problem is derived.

MSC 2010: Primary 26A33; Secondary 34A08

Keywords: fractional Hadamard-type derivatives and integrals; weighted spaces of summable and absolutely continuous functions; fractional Cauchy problem; Banach contraction principle

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About the article

Received: 2016-11-25

Accepted: 2018-03-06

Published Online: 2018-11-20

Published in Print: 2018-12-19


(Communicated by Michal Fečkan)


Citation Information: Mathematica Slovaca, Volume 68, Issue 6, Pages 1353–1366, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0186.

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