A Computational Analysis of Convection-Diffusion Model with Memory using Caputo-Fabrizio Derivative and Cubic Trigonometric B-Spline Functions

Authors

  • Imtiaz Ahmad Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional (UNITEN), Kajang 43000, Selangor, Malaysia
  • Mehwish Saleem Department of Mathematics, Islamia College Peshawar, Khyber Pakhtunkhwa, Pakistan
  • Arshed Ali Department of Mathematics, Islamia College Peshawar, Khyber Pakhtunkhwa, Pakistan
  • Aziz Khan Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia.
  • Thabet Abdeljawad Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia.

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6186

Keywords:

Caputo-Fabrizio fractional derivative, Cubic trigonometric B-spline functions, Fractional partial integro-differential equation, Convection-Diffusion process

Abstract

This paper presents the first study on computational solutions for time-fractional partial integro-differential equations (PIDE) arising from convection-diffusion processes with memory, employing the Caputo-Fabrizio fractional derivative and the cubic trigonometric B-spline differential quadrature method. First order backward finite difference formula is used to evaluate the Caputo-Fabrizio derivative, converting the PIDE into an integro-differential equation (IDE). The cubic trigonometric B-spline-based differential quadrature method is applied to approximate the spatial derivatives, transforming the IDE into a system of algebraic equations by expressing spatial derivatives as a weighted sum of function values. The weighting coefficients are obtained using an efficient tridiagonal solver. The method is validated through three test problems, and its computational efficiency, stability, and numerical convergence are analyzed. The results are also compared with those obtained using the cubic B-spline collocation method.

Author Biography

  • Imtiaz Ahmad, Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional (UNITEN), Kajang 43000, Selangor, Malaysia

    Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Imtiaz Ahmad, Mehwish Saleem, Arshed Ali, Aziz Khan, Thabet Abdeljawad

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How to Cite

A Computational Analysis of Convection-Diffusion Model with Memory using Caputo-Fabrizio Derivative and Cubic Trigonometric B-Spline Functions. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6186. https://doi.org/10.29020/nybg.ejpam.v18i2.6186