Editor in Chief - Anry Nersessian (Institute of Mathematics NAS, Armenia)
Deputy Editor - Rafayel Barkhudaryan (Institute of Mathematics NAS, Armenia)
Managing Editor - Linda Khachatryan (Institute of Mathematics NAS, Armenia)
e-mail: ajm@instmath.sci.am
According to the latest Scimago Journal Rank, Armenian Journal of Mathematics has maintained its position in Q3 with an SJR score of 0.36.
Read more about Armenian Journal of Mathematics has been recognized as a Q3 journal in SJRIn the present article, we propose a numerical resolution of the Caputo-Fabrizio temporal fractional wave equation with non-homogenous Dirichlet and Neumann functional conditions. We derive and analyze the semi- and fully discrete approximations using the introduced finite difference scheme for the time Caputo-Fabrizio derivative and the finite element scheme for the spacial derivative. Result of the existence and uniqueness of the solution is discussed, stability and error estimates are established. To support the theoretical studies, a numerical example is given.
A. Atangana, On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation. Appl. Math. Comput., 273 (2016), pp. 948-956.
A. Atangana and R.T. Alqahtani, Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation. Adv. Differ. Equ., 2016 (2016), article number 156, 13 pp.
A. Atangana and J.J. Nieto, Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel. Adv. Mech. Eng., 7 (2015), no. 10, pp. 1-7.
S.E. Bendimerad, A. Ayad, A. Bettache, S. Baghli and A.N.E.I. Ayad, A novel formula for calculating repulsive forces in horizontally aligned nonferrous cylindrical particles within an Eddy current separator. Powder Technology, 448 (2024), article number 120300, 10 pp.
S.E. Bendimerad, S. Baghli, A. Ayad and A. Tilmatine, Mutual inductance of two coaxial rectangular PCB coils incorporating magnetic layer. Journal of Electrical Engineering: The Journal of Slovak University of Technology, 72 (2021), no. 5, pp. 287-296.
M. Boutiba and S. Baghli-Bendimerad, Finite Element Approach for Some Fractional Diffusion Partial Differential Equations, Adlis Bellazma Publishing and Distribution, Algeria (Batna), 2026.
M. Boutiba, S. Baghli-Bendimerad and A. Benaïssa, Three approximations of numerical solution's by finite element method for resolving space-time partial differential equations involving fractional derivative's order. Math. Model. Eng. Probl., 9 (2022), no. 5, pp. 1179-1186.
M. Boutiba, S. Baghli-Bendimerad and N.E.H. Bouzara-Sahraoui, Numerical solution by finite element method for time Caputo-Fabrizio fractional partial diffusion equation. Advanced Mathematical Models & Applications, 9 (2024), no. 2, pp. 316-328.
M. Boutiba, S. Baghli-Bendimerad and M. Feçkan, Numeric FEM's solution for space-time diffusion partial differential equations with Caputo-Fabrizion and Riemann-Liouville fractional order's derivatives. Ann. Math. Sil., 37 (2023), no. 2, pp. 204-223.
M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel. Progr. Fract. Differ. Appl, 1 (2015), no. 2, pp. 73-85.
L.B. Feng, P. Zhuang, F. Liu and Y.T. Gu, Finite element method for space-time fractional diffusion equation. Numer. Algor., 72 (2016), pp. 749-767.
N. J. Ford, J. Xiao and Y. Yan, A finite element method for time fractional partial differential equations. Fract. Calc. App. Anal., 14 (2011), no. 3, pp. 454-474.
J.F. Gomez-Aguilar, M.G. Lopez-Lopez, V.M. Alvarado-Martinez, J. Reyes-Reyes and M. Adam-Medina, Modeling diffusive transport with a fractional derivative without singular kernel. Physica A: Stat. Mech. Appl., 447 (2016), pp. 467-481.
H. Hejazi, T. Moroney and F. Liu, A finite volume method for solving the two-sided time-space fractional advection-dispersion equation. Cent. Eur. J. Phys., 11 (2013), no. 10, pp. 1275-1283.
Y. Jiang and J. Ma, High-order finite element methods for time-fractional differential equations. J. Comput. App. Math., 235 (2011), no. 11, pp. 3285-3290.
Y. Li and C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation. J. Comput. Phys., 225 (2007), no. 2, pp. 1533-1552.
X. Li and C. Xu, A space-time spectral method for the time fractional diffusion equation. SIAM J. Numer. Anl., 47 (2009), no. 3, pp. 2108-2131.
C. Li, Z. Zhao and Y. Chen, Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion. Comput. Math. Appl., 62 (2011), no. 3, pp. 855-875.
Z. Liu, A. Cheng and X. Li, A second order Crank-Nicolson scheme for fractional Cattaneo equation based on new fractional derivative. Appl. Math. and Comput., 311 (2017), pp. 361-374.
Z. Liu, A. Cheng and X. Li, A second-order finite difference scheme for quasilinear time fractional parabolic equation based on new fractional derivative. International Journal of Computer Mathematics, 95 (2017), no. 2, pp. 396-411.
M.M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math., 172 (2004), no. 1, pp. 65-77.
E. Sousa, A second order explicit finite difference method for fractional advection diffusion equation. J. Comput. Math. App., 64 (2012), no. 10, pp. 3141-3152.
E. Sousa, Finite difference approximation for a fractional advection diffusion problem. J. Comput. Phys., 228 (2009), no. 11, pp. 4038-4054.
X. Zhang, P. Huang, X. Feng and L. Wei, Finite element method for two-dimensional time-fractional Tricomi-type equations, Numer. Methods Partial Differ. Equ., 29 (2013), no. 4, pp. 1081-1096.
Z. Zhao and C. Li, Fractional difference/finite element approximations for the time-space fractional telegraph equation. Appl. Math. Comput., 219 (2012), no. 6, pp. 2975-2988.
M. Zheng, F. Liu, I. Turner and V. Anh, A novel high order space-time spectral method for the time fractional Fokker-Planck equation. SIAM J. Sci. Comput., 37 (2015), no. 2, pp. A701-724.
P. Zhuang, F. Liu, I. Turner and Y. T. Gu, Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation. Appl. Math. Modell., 38 (2014), no. 15-16, pp. 3860-3870.
Armenian Journal of Mathematics (Armen.J.Math.) aims to publish original research papers and survey articles in all areas of mathematics, enhance the interests, talents, and achievements of all individuals in theoretical mathematics and its applications.
Armen.J.Math. accepts also review articles, short communications, conference proceedings, algorithms, PhD and doctoral theses and other items with a detailed exposition of results, proofs, numerical experiments and examples. One of the purposes is to reflect the progress of the mathematical research in Armenia and, by providing an international forum, to stimulate its further developments.
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Papers will be presented on the internet immediately after they are accepted for publication. Full-text access to all papers is available for free so as to reach the widest possible audiences.
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