Numerical Solution of Time Fractional Delay Partial Differential Equations by Perturbation Iteration Algorithm

Abstract

The aim of this research was to relate two physical effects for partial differential equations on the time-coordinate, notably the multipledelay times and fractional-derivative. Time Fractional Delay Partial Differential Equations (TFDPDEs) usually interpret some complex physical phenomenon. This study works to solve TFDPDE with shrinking in x and proportional delays in t numerically by utilizing the fractional derivative of Caputo sense in the numerical method known as Perturbation Iteration Algorithm (PIA). A few famous numerical examples have been solved using PIA and their comparison with an exact solutions is illustrated for ® = 1. Also, different values of ® have been depicted in graphical form to show their fractional behavior. The delay term k is also discussed extensively in this TFDPDE study. Numerical results show that this technique is reliable, convenient, and attractive for computational use in modern times.