Zaman-Kesirli Mertebeden Burgers Denklemi İçin Optimal Bir Parametre ile Homotopi Analiz Yönteminin Geliştirilmesi

Abstract

The aim of the study is to reduce the absolute error by determining the optimal value of this arbitrary parameter using the residual error function related to the selection of the arbitrary parameter h. Some numerical examples are solved and compared to existing results. The homotopy analysis method has been successfully implemented to Burgers equation to obtain serial solutions. On the base of the solutions obtained for the required equations, it has been shown that this method is applicable to time-fractional partial differential equations.

Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method

“…The purpose of this inquiry is to analyze the underlying notion of the technique employed by examining the given nonlinear equation (Alkan, 2022)…”

“…The exact calculation of the square RE in ODEs for the approximation of order 𝒎 is formally established as (Liao, 2010;Alkan, 2022)…”

“…A study was conducted to ascertain the most effective parameter of the proposed methodology. A range of approaches were employed to determine the value of the h parameter (Liao, 1992;Liao, 1999;Liao, 2003;Liao, 2005;Abbasbandy, 2008;Abdulaziz et al, 2008;Dehghan et al, 2009;Liao, 2010;Niu et al, 2010;Elsaid, 2011;Arafa et al, 2012;Fan et al, 2013;Freihat et al, 2013;Lu, 2014;Lu and Liu, 2014;Aslanov, 2015;Jia et al, 2017;Hariharan, 2017;Alkan, 2022).…”

The Novel Conformable Methods to Solve Conformable Time- Fractional Coupled Jaulent-Miodek System

“…Numerous methods have been put up in scholarly works to address mathematical quandaries. The methods encompassed in this set of techniques consist of the Adomian Decomposition Method (ADM) [37], the Homotopy Analysis Method (HAM) [35], the Homotopy Perturbation Method (HPM) [27][28][29], the Collocation Method [38], the Sumudu Transform Method (STM) [36], the Differential Transformation Method (DTM) [24-25, 32, 34], and the Variational Iteration Method (VIM) [26].…”

The Numerical Solutions of the Conformable Time-Fractional Noyes Field Model via a New Hybrid Method

“…The exact and numerical solutions to the fractional problems, however, have been investigated using a variety of computing approaches that have been created. Some of the utilized methods are Adomian decomposition method (ADM) [21][22][23], variational iteration method (VIM) [24], homotopy analysis method (HAM) [25][26][27][28], differential transform method (DTM) [29][30], homotopy perturbation method (HPM) [31][32][33], residual power series method (RPSM) [34][35][36], Laplace decomposition method (LDM) [37], q-homotopy analysis method (q-HAM) [38][39][40][41][42][43][44], qhomotopy analysis transform method (q-HATM) [45], fractional reduced differential transfofrm method (FRDTM) [45], conformable fractional Elzaki decomposition method (CFEDM) [46], conformable qhomotopy analysis transform method (Cq-HATM) [47], conformable Shehu homotopy perturbation method (CSHPM) [47], conformable fractional q-Shehu homotopy analysis transform method (CFq-SHATM) [48], conformable Shehu transform decomposition method (CSTDM) [48]. The main goal of this study is to come up with a new method: the conformable q-Sawi homotopy analysis transform method (Cq-SHATM).…”