Open AccessNumerical Solution of Time Fractional Delay Partial Differential Equations by Perturbation Iteration Algorithm
Author(s) -
Fareeha Sami Khan,
Mariam Sultana,
M. Khalid
Publication year - 2021
Publication title -
the punjab university journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 1016-2526
DOI - 10.52280/pujm.2021.530803
Subject(s) - mathematics , partial differential equation , fractional calculus , perturbation (astronomy) , numerical analysis , partial derivative , delay differential equation , differential equation , mathematical analysis , algorithm , physics , quantum mechanics
The aim of this research was to relate two physical effects forpartial differential equations on the time-coordinate, notably the multipledelaytimes and fractional-derivative. Time Fractional Delay Partial DifferentialEquations (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 for® = 1. Also, different values of ® have been depicted in graphical form toshow their fractional behavior. The delay term k is also discussed extensivelyin this TFDPDE study. Numerical results show that this technique isreliable, convenient, and attractive for computational use in modern times.