Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach

N. Ayazi, P. Mokhtary and B. Parsa Moghaddam

Chaos, Solitons & Fractals, 2024, vol. 181, issue C

Abstract: This paper presents a new approach for solving fractional delay differential equations of variable order using the spectral element method. The proposed method overcomes the limitations of traditional spectral methods, such as poor approximation in long intervals and inefficiency in high degrees. By introducing a variable order differentiation matrix and using basic Lagrangian functions to approximate the solution in each element, the method achieves high accuracy and efficiency. A penalty method is also applied to minimize the jump of fluxes at interface points, and the effectiveness of this approach is analyzed. Finally, three benchmark problems are solved, and the convergence analysis demonstrates the effectiveness and efficiency of the proposed method. In essence, this paper offers a significant contribution to the literature on fractional differential equations and their numerical solution methodologies.

Keywords: Fractional calculus; Variable order fractional differential equations; Delayed fractional differential equations; Nonlinear fractional differential equations; Spectral element method; Convergence analysis (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001863

DOI: 10.1016/j.chaos.2024.114635

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