Homotopy perturbation transform method for solving fractional partial differential equations with proportional delay

TL;DR

This paper introduces a hybrid analytical-numerical method combining Laplace transform and homotopy perturbation to efficiently solve time-fractional PDEs with proportional delay, demonstrated on generalized Burgers equations.

Contribution

The paper develops the homotopy perturbation transform method (HPTM) for solving fractional PDEs with delay, providing a fast-converging series solution approach.

Findings

Solutions in series form converge rapidly.

Method is reliable and effective for physical models.

Validated on three test problems with proportional delay.

Abstract

This paper deals the implementation of \emph{homotopy perturbation transform method} (HPTM) for numerical computation of initial valued autonomous system of time-fractional partial differential equations (TFPDEs) with proportional delay, including generalized Burgers equations with proportional delay. The HPTM is a hybrid of Laplace transform and homotopy perturbation method. To confirm the efficiency and validity of the method, the computation of three test problems of TFPDEs with proportional delay presented. The proposed solutions are obtained in series form, converges very fast. The scheme seems very reliable, effective and efficient powerful technique for solving various type of physical models arising in sciences and engineering.