Operational Calculus for the 1st-Level General Fractional Derivatives and Its Applications

Maryam Alkandari () and Yuri Luchko
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Maryam Alkandari: Department of Mathematics, Kuwait University, Kuwait City 12037, Kuwait
Yuri Luchko: Department of Mathematics, Physics and Chemistry, Berlin University of Applied Sciences and Technology, 13353 Berlin, Germany

Mathematics, 2024, vol. 12, issue 17, 1-23

Abstract: The 1st-level General Fractional Derivatives (GFDs) combine in one definition the GFDs of the Riemann–Liouville type and the regularized GFDs (or the GFDs of the Caputo type) that have been recently introduced and actively studied in the fractional calculus literature. In this paper, we first construct an operational calculus of the Mikusiński type for the 1st-level GFDs. In particular, it includes the operational calculi for the GFDs of the Riemann–Liouville type and for the regularized GFDs as its particular cases. In the second part of the paper, this calculus is applied for the derivation of the closed-form solution formulas to the initial-value problems for the linear fractional differential equations with the 1st-level GFDs.

Keywords: fractional calculus; 1st-level general fractional derivative; fundamental theorems of fractional calculus; operational calculus; convolution series; fractional differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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