An efficient spline technique for solving time-fractional integro-differential equations

Abbas, Muhammad; Aslam, Sadia; Abdullah, Farah Aini; Riaz, Muhammad Bilal; Gepreel, Khaled A.

doi:10.1016/j.heliyon.2023.e19307

Heliyon

2023

DOI: 10.1016/j.heliyon.2023.e19307

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An efficient spline technique for solving time-fractional integro-differential equations

Muhammad Abbas,

Sadia Aslam,

Farah Aini Abdullah

et al.

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2024

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Cited by 2 publications

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Numerical investigation of $$\Psi $$-fractional differential equations using wavelets neural networks

Rahimkhani,

Heydari

2024

Comp. Appl. Math.

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Numerical investigation of $$\Psi $$-fractional differential equations using wavelets neural networks

Rahimkhani,

Heydari

2024

Comp. Appl. Math.

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Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions

Hayat,

Abbas,

Abdullah

et al. 2024

Open Physics

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The generalization of the classical FitzHugh–Nagumo model provides a more accurate description of the physical phenomena of neurons by incorporating both nonlinearity and fractional derivatives. In this article, we present a numerical method for solving the time-fractional FitzHugh–Nagumo equation (TFFNE) in the sense of the Atangana–Baleanu fractional derivative using B-spline functions. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while θ \theta -weighted scheme is used to discretize the space directions. The efficiency of the scheme is demonstrated through numerical results and rate of convergence. The convergence order and error norms are studied at different values of the noninteger parameter, temporal directions, and spatial directions. Finally, the effectiveness of the proposed methodology is examined through the analysis of three applications.

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An efficient spline technique for solving time-fractional integro-differential equations

Cited by 2 publications

References 47 publications

Numerical investigation of $$\Psi $$-fractional differential equations using wavelets neural networks

Numerical investigation of $$\Psi $$-fractional differential equations using wavelets neural networks

Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions

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