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Finite difference method for the fractional order pseudo telegraph integro-differential equation

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order α.
Rocznik
Strony
41--54
Opis fizyczny
Bibliogr. 32 poz., rys., tab.
Twórcy
  • Art and Science Faculty, Harran University, Sanlıurfa, Turkey
autor
  • Art and Science Faculty, Harran University, Sanlıurfa, Turkey
autor
  • Art and Science Faculty, Siirt University, Siirt, Turkey
Bibliografia
  • [1] Podlubny, I. (1998). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications. Academic Press, 198.
  • [2] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations. 1st Edition, North-Holland Mathematical Studies.
  • [3] Samko, S.G., Kilbas, A.A., & Marichev, O.I. (1993). Fractional Integrals and Derivatives:
  • Theory and Applications. Langhorne: Gordon and Breach.
  • [4] Cattani, C., Srivastava, H.M., & Yang, X.J. (2016). Fractional Dynamics. Berlin: de Gruyter.
  • [5] Hilfer, R. (2000). Applications of Fractional Calculus in Physics. River Edge: World Scientific Publishing.
  • [6] Miller, K.S., & Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations. 1st ed., London: Wiley.
  • [7] Asif, N.A., Hammouch, Z., Riaz, M.B., & Bulut, H. (2018). Analytical solution of a Maxwell fluid with slip effects in view of the Caputo-Fabrizio derivative. The European Physical Journal Plus, 133(7), 1-13.
  • [8] Talib, I., Jarad, F., Mirza, M.U., Nawaz, A., & Riaz, M.B. (2021). A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations. Alexandria Engineering Journal.
  • [9] Ghanbari, B. (2021). A new model for investigating the transmission of infectious diseases in a prey-predator system using a non-singular fractional derivative. Mathematical Methods in the Applied Sciences.
  • [10] Modanli, M., & Akgul, A. (2017). Numerical solution of fractional telegraph differential equations by theta-method. The European Physical Journal Special Topics, 229, 3693-3703.
  • [11] Modanli, M., & Akgul, A. (2020). On solutions of fractional order telegraph partial differential equation by Crank-Nicholson finite difference method. Applied Mathematics and Nonlinear Sciences, 5(1), 163-170.
  • [12] Kumar, D., Singh, J., & Kumar, S. (2013). Analytic and approximate solutions of space-time fractional telegraph equations via Laplace transform. Mathematics.
  • [13] Hosseini, V.R., Chen, W., & Avazzadeh, Z. (2014). Numerical solution of fractional telegraph equation by using radial basis functions. Engineering Analysis with Boundary Elements, 38, 31-39.
  • [14] Khan, H., Shah, R., Baleanu, D., Kumam, P., & Arif, M. (2019). Analytical solution of fractional-order hyperbolic telegraph equation, using natural transform decomposition method. Electronics, 8(9).
  • [15] Veeresha, P., & Prakasha, D.G. (2018). Numerical solution for fractional model of telegraph equation by using q-HATM. Mathematics.
  • [16] Ghanbari, B. (2020). On approximate solutions for a fractional prey-predator model involving the Atangana–Baleanu derivative. Advances in Difference Equations, 2020(1), 1-24.
  • [17] Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962). An active transmission line simulating nerve axon. Proceedings of the IRE, 50(10), 2061-2070.
  • [18] Fedotov, I., Shatalov, M.Y., & Marais, J. (2016). Hyperbolic and pseudo-hyperbolic equations in the theory of vibration. Acta Mechanica, 227(11), 3315-3324.
  • [19] Chen, G., & Yang, Z. (1993). Initial value problem for a class of nonlinear pseudo-hyperbolic equations. Acta Mathematicae Applicatae Sinica, 9(2), 166-173.
  • [20] Krutitskii, P.A. (1997). An initial-boundary value problem for the pseudo-hyperbolic equation of gravity-gyroscopic waves. J. Math. Kyoto Univ., 37(2), 343-365.
  • [21] Zhao, Z., & Li, H. (2019). A continuous Galerkin method for pseudo-hyperbolic equations with variable coefficients. Journal of Mathematical Analysis and Applications, 473(2), 1053-1072.
  • [22] Riaz, M.B., Awrejcewicz, J., & Baleanu, D. (2021). Exact Solutions for Thermomagetized Unsteady Non-singularized Jeffrey Fluid: Effects of Ramped Velocity, Concentration with Newtonian Heating. Results in Physics, 104367.
  • [23] Ghanbari, B. (2021). On novel nondifferentiable exact solutions to local fractional Gardner’s equation using an effective technique. Mathematical Methods in the Applied Sciences, 44(6), 4673-4685.
  • [24] Au, V.V., Jafari, H., Hammouch, Z., & Tuan, N.H. (2021). On a final value problem for a non-linear fractional pseudo-parabolic equation. Electronic Research Archive, 29(1), 1709-1734. doi: 10.3934/era.2020088.
  • [25] Can, N.H., Kumar, D., Viet, T.V., & Nguyen, A.T. (2021). On time fractional pseudo-parabolic equations with nonlocal integral conditions. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.7196.
  • [26] Inc, M., Partohaghighi, M., Akinlar, M.A., Agarwal, P., & Chu, Y.M. (2020). New solutions of fractional-order Burger-Huxley equation. Results in Physics, 18, 103290.
  • [27] Partohaghighi, M., Bayram, M., & Baleanu, D. (2019). On numerical solution of the time fractional advection-diffusion equation involving Atangana-Baleanu-Caputo derivative. Open Physics, 17(1), 816-822.
  • [28] Parto-Haghighi, M., & Manafian, J. (2020). Solving a class of boundary value problems and fractional Boussinesq-like equation with β -derivatives by fractional-order exponential trial functions. Journal of Ocean Engineering and Science, 5(3), 197-204.
  • [29] Inc, M., Parto-Haghighi, M., Akinlar, M.A., & Chu, Y.M. (2021). New numerical solutions of fractional-order Korteweg-de Vries equation. Results in Physics, 19, 103326.
  • [30] Lundgren, L., & Mattsson, K. (2020). An efficient finite difference method for the shallow water equations. Journal of Computational Physics, 422(1), 109784.
  • [31] Li, P.W. (2020). Space-time generalized finite difference nonlinear model for solving unsteady Burgers equations. Applied Mathematics Letters, 114, 106896.
  • [32] Modanli, M. (2019). On the numerical solution for third order fractional partial differential equation by difference scheme method. An International Journal of Optimization and Control: Theories and Applications (IJOCTA), 9(3), 1-5.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b0d68ffb-bd53-4e38-8c8b-17afc20eacb8
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