A numerical method to solve higher-order fractional differential equations

TL;DR

This paper introduces a novel numerical approach for solving fractional differential equations by approximating fractional derivatives with integer-order derivatives, enabling the use of classical methods for solutions.

Contribution

The paper proposes a new approximation formula for fractional derivatives of arbitrary order, simplifying fractional differential equations into classical ones for easier solution.

Findings

The method accurately approximates fractional derivatives.

It effectively transforms fractional equations into classical differential equations.

Numerical examples demonstrate high accuracy of the approach.

Abstract

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.