Integrated Lucas and Fibonacci polynomial approach for time fractional fast and slow diffusion models

Ihteram Ali, Shamsul Arifeen, Manzoor Hussain and Sahar Ahmad Idris
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Ihteram Ali: Department of Mathematics & Statistics, Women University Swabi, Swabi 23430, KP, Pakistan2School of Mathematics & Statistics, Beijing Jiaotong University, Beijing 100044, P. R. China
Shamsul Arifeen: Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Peshawar 25000, KP, Pakistan
Manzoor Hussain: Department of Mathematics, Faculty of Science & Technology, Women University of Azad Jammu & Kashmir, Bagh, Azad Kashmir, Pakistan
Sahar Ahmad Idris: Department of Industrial Engineering, Faculty of Engineering, King Khalid University Abha, Saudi Arabia

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 09, 1-22

Abstract: This paper presents the numerical method utilized for approximate solution of fast and slow diffusion models having fractional order derivative in time. The proposed method approximates the time derivative of the model using L1-formula and applies the integrated Lucas and Fibonacci polynomial functions for approximating the unknown functions and their derivatives. Then, with the help of spatial discretization, the approximated model is converted into system of linear equations. The performance of the proposed algorithm was studied by calculating the solutions of one- and two-dimensional fast and slow diffusion models and these solutions were compared with the existing methods. The comparison illustrates that the proposed method is robust and highly efficient.

Keywords: Time-fractional diffusion equation; Caputo derivative; Lucas polynomials; Fibonacci polynomials (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183125500123

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