Dimensional consistency in fractional differential equations with non singular kernels

TL;DR

This paper presents a method to ensure dimensional consistency in fractional differential equations with non-singular kernels by using a specific change of variables.

Contribution

It introduces a simple change of variables that guarantees dimensional consistency in fractional differential equations with non-singular kernels.

Findings

The proposed change of variables ensures dimensional consistency.

An example demonstrates the effectiveness of the method.

Abstract

The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential equation. We show that by performing a simple change of variables fulfilling certain conditions ensures the consistency in physical dimensions for fractional differential equations with non singular kernels. An example of the proposed method is given.