Computational analysis of time-fractional models in energy infrastructure applications

• Main Authors: Ahmad I., Bakar A.A., Ali I., Haq S., Yussof S., Ali A.H.
• Other Authors: 57220824630
• Format: Article
• Published: Elsevier B.V. 2024
• Subjects: Caputo derivative; Convection-diffusion equation; Energy infrastructure; Fibonacci polynomials; Finite differences; Lucas polynomials; Diffusion in liquids; Heat convection; Partial differential equations; Polynomials; Caputo derivatives; Computational analysis; Convection-diffusion equations; Energy infrastructures; Finite difference; Fractional model; Infrastructure applications; Luca polynomial; One-dimensional; Numerical methods

In this paper, we propose an effective numerical method to solve the one- and two-dimensional time-fractional convection-diffusion equations based on the Caputo derivative. The presented approach employs a hybrid method that combines Lucas and Fibonacci polynomials with the Caputo derivative definition. The main objective is to transform the problem into a time-discrete form utilizing the Caputo derivative technique and then approximate the function's derivative using Fibonacci polynomials. To evaluate the efficiency and accuracy of the proposed technique, we apply it to one- and two-dimensional problems and compare the results with the exact as well as with existing methods in recent literature. The comparison demonstrates that the proposed approach is highly efficient, accurate and ease to implement. � 2023 The Author(s)