General Fractional Integrals and Derivatives with the Sonine Kernels

Yuri Luchko
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Yuri Luchko: Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany

Mathematics, 2021, vol. 9, issue 6, 1-17

Abstract: In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes and particular cases are discussed. In particular, we introduce a class of the Sonine kernels that possess an integrable singularity of power function type at the point zero. For the general fractional integrals and derivatives with the Sonine kernels from this class, two fundamental theorems of fractional calculus are proved. Then, we construct the n -fold general fractional integrals and derivatives and study their properties.

Keywords: Sonine kernel; Sonine condition; general fractional derivative; general fractional integral; n-fold general fractional derivative; n-fold general fractional integral; fundamental theorems of Fractional Calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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