Abstract
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.
Highlights
Fractional calculus has many applications in physics and has attracted several researchers
We investigated the homotopy perturbation ρ-Laplace transform method for solving the fractional diffusion equation and the fractional diffusion-reaction equation described by the Caputo generalized fractional derivative
We proved our method is useful of getting the approximate solutions of the fractional diffusion equation and the fractional diffusion-reaction equation
Summary
Fractional calculus has many applications in physics and has attracted several researchers. In Reference [22], Delgado et al used the Laplace homotopy analysis for getting the approximate solutions of the linear partial differential equations described by the Caputo–Fabrizio fractional derivative and the Atangana–Baleanu fractional derivative. We investigated the homotopy perturbation ρ-Laplace transform method for solving the fractional diffusion equation and the fractional diffusion-reaction equation described by the Caputo generalized fractional derivative.
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