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Dimensional consistency in fractional differential equations with non singular kernels

Gabriel Gonzalez

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.

Dimensional consistency in fractional differential equations with non singular kernels

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.

Paper Structure

This paper contains 9 sections, 25 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Dimensional consistency in fractional derivative operators
  3. Linearity.
  4. Derivative of a Constant.
  5. Limit Cases.
  6. Laplace Transform.
  7. Example: Analysis of an RC circuit
  8. Conclusions
  9. Acknowledgement

Figures (2)

  • Figure 1: RC circuit.
  • Figure 2: The figure shows the voltage across the capacitor