Operational calculus for the general fractional derivative and its applications-Reference-Cited by-同舟云学术

Operational calculus for the general fractional derivative and its applications

Published:2021-04-01 Issue:2 Volume:24 Page:338-375
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Luchko Yuri¹

Affiliation:

1. Dept. of Mathematics , Physics, and Chemistry Beuth Technical University of Applied Sciences Berlin , Luxemburger Str. 10 , Berlin - 13353 , Germany

Abstract

Abstract In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of power function type at the point zero. Both particular cases and compositions of these operators are discussed. Then we proceed with a construction of an operational calculus of the Mikusiński type for the general fractional derivatives with the Sonine kernels. This operational calculus is applied for analytical treatment of some initial value problems for the fractional differential equations with the general fractional derivatives. The solutions are expressed in form of the convolution series that generalize the power series for the exponential and the Mittag-Leffler functions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2021-0016/pdf

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