A Comment on the Conformable Euler Finite Difference Method

TL;DR

This paper critically examines the conformable Euler finite difference method for fractional differential equations, revealing its limitations to integer derivatives and proposing a modified approach for fractional problems.

Contribution

The paper identifies the limitations of the conformable Euler method for fractional derivatives and introduces a modified method applicable to fractional initial value problems.

Findings

Conformable Euler method is valid only for integer derivatives.

A modified conformable Euler method is derived for fractional derivatives.

The new method extends applicability to fractional initial value problems.

Abstract

A method, recently advanced as the conformable Euler method, a general method for the finite difference discretization of fractional initial value problems for fractions in (0, 1], is shown to be valid only for the integer derivative. The property of the conformable fractional derivative used to show this limitation of the method is used, together with the integer definition of the derivative, to derive a modified conformable Euler method for the initial value problem considered.