A fractional model of the diffusion equation and its analytical solution using Laplace transform | Zendy

Sunil Kumar | Zendy; Ahmet Yıldırım | Zendy; Yasir Khan | Zendy; Leilei Wei | Zendy

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A fractional model of the diffusion equation and its analytical solution using Laplace transform

Author(s) -

Sunil Kumar,

Ahmet Yıldırım,

Yasir Khan,

Leilei Wei

Publication year - 2012

Publication title -

scientia iranica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.299

H-Index - 51

eISSN - 2345-3605

pISSN - 1026-3098

DOI - 10.1016/j.scient.2012.06.016

Subject(s) - laplace transform , diffusion equation , inverse laplace transform , diffusion , mellin transform , laplace–stieltjes transform , mathematics , fractional calculus , green's function for the three variable laplace equation , mathematical analysis , laplace's equation , physics , fourier transform , thermodynamics , fractional fourier transform , partial differential equation , fourier analysis , economy , economics , service (business)

In this study, the homotopy perturbation transform method (HPTM) is performed to give analytical solutions of the time fractional diffusion equation. The HPTM is a combined form of the Laplace transform and homotopy perturbation methods. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation. A solution has been plotted for different values of α., and some numerical illustrations are given

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