Approximate Solutions Of Time-fractional Fourth-order Differential Equations With Variable Coefficients

Xiaohua  Wang

doi:10.6180/jase.202309_26(9).0003

Approximate Solutions Of Time-fractional Fourth-order Differential Equations With Variable Coefficients

Civil Engineering

$Approximate Solutions Of Time-fractional Fourth-order Differential Equations With Variable Coefficients$

Xiaohua Wang

Teaching Affairs Office, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang 322100, China

Received: May 15, 2022
Accepted: August 5, 2022
Publication Date: November 24, 2022

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202309_26(9).0003

ABSTRACT

In this work, the homotopy analysis method (HAM) is proposed to obtain semi-analytical solutions of timefractional fourth-order partial differential equations (PDEs) with variable coefficients, by the Caputo fractional derivative in the time direction. Convergence of this method has been considered and some illustrative examples show the effect of changing homotopy auxiliary parameter ¯h on the convergence of the approximate solution. Comparison of obtained results with other techniques such as Adomian decomposition method and modified variational iteration method, in literature demonstrate that our utilized method is powerful and reliable technique. Moreover, the absolute errors of considered problems in the integer differential order cases, show that the reported results are very closed to the exact solutions.

Keywords: Homotopy analysis method; time-fractional fourth-order equation; variable coefficient; Caputo fractional derivative.

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