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.
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