Homotopy decomposition method for solving higher-order time-fractional diffusion equation via modified beta derivative
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 differ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2018
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| Online Access: | http://journalarticle.ukm.my/12672/ http://journalarticle.ukm.my/12672/ http://journalarticle.ukm.my/12672/1/33%20Salah%20Abuasad.pdf |
| Summary: | 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. |
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