Multi-Kernel General Fractional Calculus of Arbitrary Order

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.