Vol. 13(1). Jan. 2022, No. 5, pp. 42-57.

FRACTIONAL DIFFUSION EQUATION WITH REACTION TERM DESCRIBED BY THE CAPUTO-LIOUVILLE GENERALIZED FRACTIONAL DERIVATIVE
Vol. 13(1) Jan. 2022, No. 5, pp. 42-57
N. SENE

Abstract

In this present paper, we investigate a new model for fluids in the context of fractional calculus. We study the fractional diffusion reaction equations. In our model, the reaction term describes a fractional heat equation. We present the qualitative properties of the introduced models. We propose the solution of the fractional diffusion reaction equations represented by the Caputo-Liouville generalized fractional derivative. We combine in this work the Laplace transformation and the Fourier transformation for getting the solutions of the introduced models. Our contributions are to analyze the impact of the fractional-order derivative and the reaction term on the diffusion processes. We also interpret the effect of the Prandtl number P r on the diffusion processes.


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