Multi-Kernel General Fractional Calculus of Arbitrary Order

Vasily E. Tarasov ()
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Vasily E. Tarasov: Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia

Mathematics, 2023, vol. 11, issue 7, 1-32

Abstract: An extension of the general fractional calculus (GFC) of an arbitrary order, proposed by Luchko, is formulated. This extension is also based on a multi-kernel approach, in which the Laplace convolutions of different Sonin kernels are used. The proposed multi-kernel GFC of an arbitrary order is also considered for the case of intervals ( a , b ) where − ∞ < a < b ≤ ∞ . Examples of multi-kernel general fractional operators of arbitrary orders are proposed.

Keywords: general fractional calculus; fractional derivatives; fractional integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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