Numerical Solution of a Wave Partial Differential Equation With the Caputo-Fabrizio Time-Fractional Derivative Using the Finite Element Method Under Non-Homogenous Dirichlet and Neumann Boundary Conditions

Boutiba, M.; Baghli-Bendimerad, S.; Sabit, S.

Numerical Solution of a Wave Partial Differential Equation With the Caputo-Fabrizio Time-Fractional Derivative Using the Finite Element Method Under Non-Homogenous Dirichlet and Neumann Boundary Conditions

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Title: Numerical Solution of a Wave Partial Differential Equation With the Caputo-Fabrizio Time-Fractional Derivative Using the Finite Element Method Under Non-Homogenous Dirichlet and Neumann Boundary Conditions

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1829-1163

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Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան

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1-20

Abstract:

In the present article, we propose a numerical reso-lution of the Caputo–Fabrizio temporal fractionalwaveequationwith non-homogenous Dirichlet and Neumann functional con-ditions. We derive and analyze the semi- and fully discrete ap-proximations using the introduced finite difference scheme for thetime Caputo–Fabrizio derivative and the finite element schemefor the spacial derivative. Result of the existence and unique-ness of the solution is discussed, stability and error estimatesare established. To support the theoretical studies, a numericalexample is given.

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oai:arar.sci.am:440028

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Electronic Open Access Publication of the National Academy of Sciences of Armenia

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ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան

Subject and keywords:

Mathematics Finite Element Method Caputo–Fabrizio Derivative TimeFractional Wave Equation Error Estimates

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Sep 4, 2026

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Sep 4, 2026

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https://arar.sci.am/publication/474421

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Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես

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Boutiba, M., Numerical Solution of a Wave Partial Differential Equation With the Caputo-Fabrizio Time-Fractional Derivative Using the Finite Element Method Under Non-Homogenous Dirichlet and Neumann Boundary Conditions	Sep 4, 2026

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Title: Numerical Solution of a Wave Partial Differential Equation With the Caputo-Fabrizio Time-Fractional Derivative Using the Finite Element Method Under Non-Homogenous Dirichlet and Neumann Boundary Conditions

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