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Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences

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  • Alessandra Jannelli

    (Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy)

Abstract

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.

Suggested Citation

  • Alessandra Jannelli, 2020. "Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:215-:d:318176
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    Cited by:

    1. Ahmed Salem & Lamya Almaghamsi, 2023. "Solvability of Sequential Fractional Differential Equation at Resonance," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    2. Mikel Brun & Fernando Cortés & María Jesús Elejabarrieta, 2021. "Transient Dynamic Analysis of Unconstrained Layer Damping Beams Characterized by a Fractional Derivative Model," Mathematics, MDPI, vol. 9(15), pages 1-18, July.

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