Special Functions of Fractional Calculus in Form of Convolution Series and their Applications

2021/08/12 by Luchko, Yuri · 1 citation
#26A33 #26B30 #44A10 #45E10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.05668

Abstract

In this paper, we first discuss the convolution series that are generated by the Sonine kernels from a class of functions continuous on the real positive semi-axis that have an integrable singularity of power function type at the point zero. These convolution series are closely related to the general fractional integrals and derivatives with the Sonine kernels and represent a new class of the special functions of Fractional Calculus. The Mittag-Leffler functions as solutions to the fractional differential equations with the fractional derivatives of both Riemann-Liouville and Caputo types are particular cases of the convolution series generated by the Sonine kernel κ(t) = t^α-1/Γ(α), 0

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• Parametric General Fractional Calculus: Nonlocal Operators Acting on Function with Respect to Another Function

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