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Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation

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Laboratoire Lmdan, Département de Mathématiques de la Décision, Faculté des Sciences Economiques et Gestion, Université Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal
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Centre de Recherche Economique Appliquées, Laboratoire Ingénierie Financiére et Economique (LIFE), Faculté des Sciences Économiques et de Gestion, Université Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(2), 14; https://doi.org/10.3390/fractalfract3020014
Received: 5 March 2019 / Revised: 25 March 2019 / Accepted: 26 March 2019 / Published: 27 March 2019
In this paper, the approximate solutions of the fractional diffusion equations described by the fractional derivative operator were investigated. The homotopy perturbation Laplace transform method of getting the approximate solution was proposed. The Caputo generalized fractional derivative was used. The effects of the orders α and ρ in the diffusion processes was addressed. The graphical representations of the approximate solutions of the fractional diffusion equation and the fractional diffusion-reaction equation both described by the Caputo generalized fractional derivative were provided. View Full-Text
Keywords: fractional diffusion equatiion; fractional diffusion-reaction equation; Caputo generalized fractional derivative; approximate solution fractional diffusion equatiion; fractional diffusion-reaction equation; Caputo generalized fractional derivative; approximate solution
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Sene, N.; Fall, A.N. Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation. Fractal Fract 2019, 3, 14.

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