Multi-Kernel General Fractional Calculus of Arbitrary Order - Vasily E. Tarasov (Mathematics, 2023)
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 <semantics>(a,b)</semantics> where <semantics>−<mspace width="0.166667em"></mspace>∞<mspace width="0.166667em"></mspace><<mspace width="0.166667em"></mspace>a<mspace width="0.166667em"></mspace><<mspace width="0.166667em"></mspace>b<mspace width="0.166667em"></mspace>≤<mspace width="0.166667em"></mspace>∞</semantics>. Examples of multi-kernel general fractional operators of arbitrary orders are proposed.