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A computational method for time fractional partial integro-differential equations

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a class of time fractional partial integro-differential equations (FPIDEs) with initial conditions is studied. Some operational matrices are used to reduce a FPIDE problem to a system of algebraic equations with special properties. The resulted system is solved to give an approximate solution to the problem. Error estimation is also discussed for the approximate solution. Finally, some numerical examples are given to show the accuracy of the proposed method.
Wydawca
Rocznik
Strony
315--323
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
  • Department of Mathematics, Shahed University, Tehran, Iran
  • Department of Mathematics, Shahed University, Tehran, Iran
autor
  • Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Bibliografia
  • [1] M. H. AliAbadi and S. Shahmorad, A matrix formulation of the tau method for Fredholm and Volterra linear integro-differential equations, Korean J. Comput. Appl. Math. 9 (2002), no. 2, 497-507.
  • [2] K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Math. 2004, Springer, Berlin, 2010.
  • [3] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, 2000.
  • [4] M. Inc, The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method, J. Math. Anal. Appl. 345 (2008), no. 1, 476-484.
  • [5] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
  • [6] Y. Li, Solving a nonlinear fractional differential equation using Chebyshev wavelets, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 9, 2284-2292.
  • [7] J. T. Machado, V. Kiryakova and F. Mainardi, Recent history of fractional calculus, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 3, 1140-1153.
  • [8] Z. Meng, L. Wang, H. Li and W. Zhang, Legendre wavelets method for solving fractional integro-differential equations, Int. J. Comput. Math. 92 (2015), no. 6, 1275-1291.
  • [9] M. Mojahedfar and A. Tari Marzabad, Solving two-dimensional fractional integro-differential equations by Legendre wavelets, Bull. Iranian Math. Soc. 43 (2017), no. 7, 2419-2435.
  • [10] P. Mokhtary, F. Ghoreishi and H. M. Srivastava, The Müntz-Legendre Tau method for fractional differential equations, Appl. Math. Model. 40 (2016), no. 2, 671-684.
  • [11] D. Nazari and S. Shahmorad, Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions, J. Comput. Appl. Math. 234 (2010), no. 3, 883-891.
  • [12] Z. M. Odibat and S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul. 7 (2006), no. 1, 27-34.
  • [13] K. Oldham, Fractional differential equations in electrochemistry, Adv. Eng. Softw. 41 (2010), 9-17.
  • [14] M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Lect. Notes Electr. Eng. 84, Springer, Dordrecht, 2011.
  • [15] E. L. Ortiz and K.-S. Pun, Numerical solution of nonlinear partial differential equations with the Tau method, J. Comput. Appl. Math. 12-13 (1985), 511-516.
  • [16] E. L. Ortiz and H. Samara, An operational approach to the tau method for the numerical solution of nonlinear differential equations, Computing 27 (1981), no. 1, 15-25.
  • [17] J. A. Rad, S. Kazem, M. Shaban, K. Parand and A. Yildirim, Numerical solution of fractional differential equations with a tau method based on Legendre and Bernstein polynomials, Math. Methods Appl. Sci. 37 (2014), no. 3, 329-342.
  • [18] Y. A. Rossikhin and M. V. Shitikova, Application of fractional calculus for dynamic problems of solid mechanics: Novel trends and recent result, Appl. Mech. Rev. 63 (2010), 1-52.
  • [19] A. Tari, M. Y. Rahimi, S. Shahmorad and F. Talati, Development of the tau method for the numerical solution of two-dimensional linear Volterra integro-differential equations, Comput. Methods Appl. Math. 9 (2009), no. 4, 421-435.
  • [20] S. K. Vanani and A. Aminataei, Operational Tau approximation for a general class of fractional integro-differential equations, Comput. Appl. Math. 30 (2011), no. 3, 655-674.
  • [21] Q. Wang, Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method, Appl. Math. Comput. 182 (2006), no. 2, 1048-1055.
  • [22] J. L. Wu, A wavelet operational method for solving fractional partial differential equations numerically, Appl. Math. Comput. 214 (2009), no. 1, 31-40.
  • [23] L. Zhu and Q. Fan, Numerical solution of nonlinear fractional-order-Volterra integro-differential equations by SCW, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), no. 5, 1203-1213.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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