# Kaedah penguraian homotopi bagi menyelesaikan persamaan resapan pecahan-masa peringkat tinggi menerusi terbitan terubah suai beta

Translated title of the contribution: Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative

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2 Citations (Scopus)

### Abstract

In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement.

Original language Malay 2899-2905 7 Sains Malaysiana 47 11 https://doi.org/10.17576/jsm-2018-4711-33 Published - 1 Nov 2018

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decomposition
iteration
integral equations
differential equations
perturbation

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### Cite this

In: Sains Malaysiana, Vol. 47, No. 11, 01.11.2018, p. 2899-2905.

Research output: Contribution to journalArticle

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title = "Kaedah penguraian homotopi bagi menyelesaikan persamaan resapan pecahan-masa peringkat tinggi menerusi terbitan terubah suai beta",
abstract = "In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement.",
keywords = "Beta derivative, Fractional differential equation, Fractional diffusion equation, Homotopy decomposition method",
author = "Salah Abuasad and Ishak Hashim",
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T1 - Kaedah penguraian homotopi bagi menyelesaikan persamaan resapan pecahan-masa peringkat tinggi menerusi terbitan terubah suai beta

AU - Hashim, Ishak

PY - 2018/11/1

Y1 - 2018/11/1

N2 - In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement.

AB - In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement.

KW - Beta derivative

KW - Fractional differential equation

KW - Fractional diffusion equation

KW - Homotopy decomposition method

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