New approaches for solving systems of time-fractional partial differential equations

Abstract

The main goal of this thesis is to propose an effectual approach, called Khalouta-Daftardar-Jafari approach, which is the collaboration of the Khalouta transform in the sense of the Caputo fractional derivative and the iterative approach used by Daftardar-Gejji and Jafari for finding approximate and closed-form solutions to systems of nonlinear time-fractional partial differential equations, especially the system of nonlinear time-fractional Burgers equations. The advantage of this new approach, which we have planned, lies in its computational simplicity and superior accuracy, which allows us to approximate the final result.