ANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIED q -HATM

Nehad Ali Shah; Praveen Agarwal; Jae Dong Chung; Saad Althobaiti; Samy Sayed; A. F. Aljohani; Mohamed Alkafafy

doi:10.1142/S0218348X22400126

ANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIED q -HATM

Nehad Ali Shah, Praveen Agarwal, Jae Dong Chung, Saad Althobaiti, Samy Sayed, A. F. Aljohani, Mohamed Alkafafy

Department of Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, the q-homotopy analysis transform technique is implemented to analyze the solution of fractional-order Burgers and diffusion equations with the help of Caputo operator. The results of the proposed method are shown and analyzed with the help of figures. This approach is used to determine the solution in a convergent sequence and illustrate the q-homotopy analysis transform technique solutions convergence to the exact result. Several examples showed the reliability and simplicity of the technique and highlighted the significance of this work. Therefore, the proposed method is successful in investigating other fractional-order linear and nonlinear partial differential equations.

Original language	American English
Journal	Fractals
Volume	30
Issue number	1
DOIs	https://doi.org/10.1142/S0218348X22400126
State	Published - 1 Feb 2022

Keywords

Burgers' and Diffusion Equations
Caputo Derivatives
Elzaki Transform
q-Homotopy Analysis Transform Method

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10.1142/S0218348X22400126

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title = "ANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIED q -HATM",

abstract = "In this paper, the q-homotopy analysis transform technique is implemented to analyze the solution of fractional-order Burgers and diffusion equations with the help of Caputo operator. The results of the proposed method are shown and analyzed with the help of figures. This approach is used to determine the solution in a convergent sequence and illustrate the q-homotopy analysis transform technique solutions convergence to the exact result. Several examples showed the reliability and simplicity of the technique and highlighted the significance of this work. Therefore, the proposed method is successful in investigating other fractional-order linear and nonlinear partial differential equations.",

keywords = "Burgers' and Diffusion Equations, Caputo Derivatives, Elzaki Transform, q-Homotopy Analysis Transform Method",

author = "Shah, {Nehad Ali} and Praveen Agarwal and Chung, {Jae Dong} and Saad Althobaiti and Samy Sayed and Aljohani, {A. F.} and Mohamed Alkafafy",

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T1 - ANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIED q -HATM

AU - Shah, Nehad Ali

AU - Agarwal, Praveen

AU - Chung, Jae Dong

AU - Althobaiti, Saad

AU - Sayed, Samy

AU - Aljohani, A. F.

AU - Alkafafy, Mohamed

PY - 2022/2/1

Y1 - 2022/2/1

N2 - In this paper, the q-homotopy analysis transform technique is implemented to analyze the solution of fractional-order Burgers and diffusion equations with the help of Caputo operator. The results of the proposed method are shown and analyzed with the help of figures. This approach is used to determine the solution in a convergent sequence and illustrate the q-homotopy analysis transform technique solutions convergence to the exact result. Several examples showed the reliability and simplicity of the technique and highlighted the significance of this work. Therefore, the proposed method is successful in investigating other fractional-order linear and nonlinear partial differential equations.

AB - In this paper, the q-homotopy analysis transform technique is implemented to analyze the solution of fractional-order Burgers and diffusion equations with the help of Caputo operator. The results of the proposed method are shown and analyzed with the help of figures. This approach is used to determine the solution in a convergent sequence and illustrate the q-homotopy analysis transform technique solutions convergence to the exact result. Several examples showed the reliability and simplicity of the technique and highlighted the significance of this work. Therefore, the proposed method is successful in investigating other fractional-order linear and nonlinear partial differential equations.

KW - Burgers' and Diffusion Equations

KW - Caputo Derivatives

KW - Elzaki Transform

KW - q-Homotopy Analysis Transform Method

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DO - 10.1142/S0218348X22400126

M3 - Article

VL - 30

JO - Fractals

JF - Fractals

SN - 0218-348X

IS - 1

ER -

ANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIED q -HATM

Abstract

Keywords

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