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Volume 12
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Article

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

by
Maryam Alkandari
1,* and
Yuri Luchko
2
1
Department of Mathematics, Kuwait University, Kuwait City 12037, Kuwait
2
Department of Mathematics, Physics and Chemistry, Berlin University of Applied Sciences and Technology, 13353 Berlin, Germany
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(17), 2626; https://doi.org/10.3390/math12172626 (registering DOI)
Submission received: 17 July 2024 / Revised: 18 August 2024 / Accepted: 22 August 2024 / Published: 24 August 2024
Versions Notes

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 fractional calculus; 1st-level general fractional derivative; fundamental theorems of fractional calculus; operational calculus; convolution series; fractional differential equations

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MDPI and ACS Style

Alkandari, M.; Luchko, Y. Operational Calculus for the 1st-Level General Fractional Derivatives and Its Applications. Mathematics 2024, 12, 2626. https://doi.org/10.3390/math12172626

AMA Style

Alkandari M, Luchko Y. Operational Calculus for the 1st-Level General Fractional Derivatives and Its Applications. Mathematics. 2024; 12(17):2626. https://doi.org/10.3390/math12172626

Chicago/Turabian Style

Alkandari, Maryam, and Yuri Luchko. 2024. "Operational Calculus for the 1st-Level General Fractional Derivatives and Its Applications" Mathematics 12, no. 17: 2626. https://doi.org/10.3390/math12172626

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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