Operational Calculus for the General Fractional Derivatives of Arbitrary Order

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 derivative...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-05, Vol.10 (9), p.1590
Main Authors: Al-Kandari, Maryam, Hanna, Latif A-M., Luchko, Yuri
Format: Article
Language:English
Subjects:
Algebra
Calculus
convolution series
Derivatives
Fractional calculus
fundamental theorems of fractional calculus
general fractional derivative of arbitrary order
general fractional integral
Integrals
Mathematical analysis
Mathematicians
Operational calculus
Operators (mathematics)
Quotients
Singularity (mathematics)
Sonine kernel
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10091590