Solution of the Generalized Burgers Equation Using Homotopy Perturbation Method with General Fractional Derivative

Abstract

This research paper introduces the generalized Burgers equation, a mathematical model defined using the general fractional derivative, the most recent operator in fractional calculus. The general fractional derivative can be reduced into three well-known operators, providing a more tractable form of the equation. We apply the homotopy perturbation method (HPM), a powerful analytical technique, to obtain the solution of the generalized Burgers equation. The results are illustrated using a practical example, and we present an analysis of the three reduced operators. In addition, a graphical analysis is provided to visualize the behavior of the solution. This study sheds light on the application of the homotopy perturbation method and the general fractional derivative in solving the generalized Burgers equation, contributing to the field of nonlinear differential equations.

Keywords

• fractional Burgers equation
• generalized fractional derivative
• fixed point theorem