A new modification of the reduced differential transform method for nonlinear fractional partial differential equations

Abstract

The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.

Khalouta transform and applications to Caputo-fractional differential equations

“…Although the concept finds its roots in the works of Euler, Laplace and Fourier in the 18th and 19th centuries, it has gained significant attention in recent years for its applications in diverse scientific and engineering fields. Solving fractional differential can be more challenging than solving traditional differential equations, and various numerical and analytical method [1][2][3][4][5] have been developed for this purpose. An integral transform is an operation that takes a function and maps it to another function through integration.…”

Combination ofShehudecomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations

“…This technique is modified with the help of Shehu transformation so the modified technique is the Shehu decomposition method. This method is applied to the nonhomogeneous fractional differential equations [20][21][22].…”

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

“…To mention a few, we have the homotopy perturbation method (HPM) [6], the Adomian decomposition method (ADM) [7], the Laplace decomposition method (LDM) [8], the homotopy perturbation transform method (HPTM) [9], and so on. Besides using the Laplace-type integral transform [10,11], some new efficient iterative techniques with the Caputo fractional derivative [12] and Atangana-Baleanu fractional derivative [13] are developed, for example, see [14][15][16][17][18][19][20][21][22][23][24][25]. Those iterative algorithms are successfully applied to many applications in applied physical science.…”