Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications

被引：0
作者：
Hafiz Muhammad Fahad
Arran Fernandez
机构：
[1] Faculty of Arts and Sciences Eastern Mediterranean University,Department of Mathematics
来源：
Fractional Calculus and Applied Analysis | 2021年 / 24卷
关键词：
fractional differential equations; operational calculus; Mikusinski operational calculus; fractional calculus with respect to functions; Primary 26A33; Secondary 44A40; 34A08; 33E12;
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学科分类号：
摘要：
Mikusiński’s operational calculus is a formalism for understanding integral and derivative operators and solving differential equations, which has been applied to several types of fractional-calculus operators by Y. Luchko and collaborators, such as for example [26], etc. In this paper, we consider the operators of Riemann–Liouville fractional differentiation of a function with respect to another function, and discover that the approach of Luchko can be followed, with small modifications, in this more general setting too. The Mikusiński’s operational calculus approach is used to obtain exact solutions of fractional differential equations with constant coefficients and with this type of fractional derivatives. These solutions can be expressed in terms of Mittag-Leffler type functions.
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页码：518 / 540
页数：22
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