Operational Calculus for the General Fractional Derivatives of Arbitrary Order

Maryam Al-Kandari, Latif A-M. Hanna and Yuri Luchko
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Maryam Al-Kandari: Department of Mathematics, Kuwait University, Kuwait City 12037, Kuwait
Latif A-M. Hanna: Department of Mathematics, Kuwait University, Kuwait City 12037, Kuwait
Yuri Luchko: Department of Mathematics, Physics, and Chemistry, Berlin University of Applied Sciences and Technology, 10587 Berlin, Germany

Mathematics, 2022, vol. 10, issue 9, 1-17

Abstract: In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin. In particular, we introduce the sequential fractional derivatives of this type and derive an explicit formula for their projector operator. The main contribution of this paper is a construction of an operational calculus of Mikusiński type for the general fractional derivatives of arbitrary order. In particular, we present a representation of the m -fold sequential general fractional derivatives of arbitrary order as algebraic operations in the field of convolution quotients and derive some important operational relations.

Keywords: Sonine kernel; general fractional integral; general fractional derivative of arbitrary order; fundamental theorems of fractional calculus; operational calculus; convolution series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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