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Open AccessFeature PaperArticle

Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences

Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy
Mathematics 2020, 8(2), 215; https://doi.org/10.3390/math8020215
Received: 13 January 2020 / Revised: 4 February 2020 / Accepted: 5 February 2020 / Published: 8 February 2020
This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF–ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems.
Keywords: fractional advection-diffusion-reaction equation; Caputo fractional derivative; unconditionally stable finite difference method; dynamics in packed bed column fractional advection-diffusion-reaction equation; Caputo fractional derivative; unconditionally stable finite difference method; dynamics in packed bed column
MDPI and ACS Style

Jannelli, A. Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences. Mathematics 2020, 8, 215.

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