Homotopy perturbation transform method for solving fractional partial differential equations with proportional delay
For researchers in fractional calculus and applied mathematics, this is an incremental application of an existing hybrid method to a specific class of equations.
The paper applies the homotopy perturbation transform method (HPTM) to solve time-fractional partial differential equations with proportional delay, including generalized Burgers equations. The method yields rapidly converging series solutions, demonstrated on three test problems.
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.