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

摘要

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