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

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

doi:10.1016/j.chaos.2024.114635

Chaos, Solitons & Fractals

2024

DOI: 10.1016/j.chaos.2024.114635

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

N. Ayazi,

P. Mokhtary,

B. Parsa Moghaddam

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2024

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Cited by 2 publications

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Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

Atta,

Youssri

2024

Math Methods in App Sciences

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In this study, we utilize a specific combination of orthogonal Gegenbauer polynomials as basis functions that satisfy homogeneous boundary conditions in the spatial variable and homogeneous initial conditions in the temporal variable. We derive an expression for the fractional derivative of the temporal basis and another expression for the second‐order derivative of the spatial basis. Subsequently, we discretize the nonlinear Fisher problem using the spectral collocation method to transform the problem into the solution of a nonlinear system of algebraic equations. We then solve this resulting system using Newton's method with an initial guess approaching zero. Furthermore, we conduct an error analysis of the proposed method and assess its applicability through three test problems, providing comparisons for validation.

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Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

Atta,

Youssri

2024

Math Methods in App Sciences

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Fractional-order identification system based on Sundaresan’s technique

Campos,

Ayres,

de Bessa

et al. 2024

Chaos, Solitons & Fractals

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

Cited by 2 publications

References 37 publications

Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

Fractional-order identification system based on Sundaresan’s technique

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