A numerical scheme for a generalized fractional derivative with variable order

Abstract

The aim of this paper is to present an approximation formula for the Caputo fractional derivative of variable order, with dependence on an arbitrary kernel. For special cases of this kernel function, or the fractional order being constant, we recover some known formulas. This numerical method involves only integer-order derivatives, so any fractional problem can be approximated by an integer-order problem. Some numerical simulations end the paper, showing the effectiveness of our procedure.