Comparative Analysis of Natural Transform Decomposition Method and New Iterative Method for Fractional Foam Drainage Problem and Fractional Order Modified Regularized Long-Wave Equation

Abstract

In this paper, a comparative study of natural transform decomposition method and new iterative method is presented. The proposed methods are tested upon nonlinear fractional order foam drainage problem and fractional order modified regularized long-wave equation. The solutions obtained by the proposed methods have been compared with the classical solutions and the solution obtained by Adomian decomposition method. Furthermore, the efficiency and reliability of the proposed methods are shown with the help of numerical and graphical results. The fractional order derivatives are defined in Caputo’s sense whose order belongs to the closed interval [0,1]. The results reveal that the methods are quickly convergent and yield encouraging results.

Another hybrid approach for solving monotone operator equations and application to signal processing

“…Note that Equation ( 6) is defined such that the direction always satisfies the sufficient descent condition if G (k) ∶= g (k) . In addition, the vector 𝑦 (k−1) in ( 5) is replaced with u (k−1) in (7) such that 𝛽 (k) 1 and 𝛽 (k) 2 are well defined. Remark 1.…”

“…The appearance of problem (1) in various field of research and applications such as power flow equation, chemical equilibrium systems, compressive sensing, [1][2][3][4][5] and several others [6][7][8][9] have motivated several studies on effective methods for finding solutions to (1).…”

Novel Analysis of Nonlinear Seventh Order Kaup-Kupershmidt Equation via the Caputo Operator

“…A range of scientiőc topics has been modeled using partial differential equations, particularly nonlinear ones. Because of FPDEs, scientists were able to discover and model a extensive assortment of important and useful physical challenges along with their effort in the physical sciences [39,40]. The signiőcance of obtaining approximate has always been remarked.…”

Analytical Approximate Solution of the Fractional Order Biological Population Model by Using Natural Transform

“…The proposed techniques have been recently applied by Nawaz et al for solving noninteger order differential equations [13]. Many other researchers have applied NIM and natural transform for handling the FDEs [14][15][16][17]. In this article, we will consider fractional biological population model (FBPM) as [18]…”