Numerical Solution of Time Fractional Parabolic Differential Equations

  • Authors

    • T. R.Ramesh Rao
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.26117
  • Reduced differential transform, fractional derivatives, Riemann-Liouvilles fractional derivatives.
  • Abstract

    In this paper, we study the coupling of an approximate analytical technique called reduced differential transform (RDT) with fractional complex transform. The present method reduces the time fractional differential equations in to integer order differential equations. The fractional derivatives are defined in Jumaries modified Riemann-Liouville sense. Result shows that the present technique is effective and powerful for handling the fractional order differential equations.

     

  • References

    1. [1] Kilbas AA, Srivastava HM & Trujillo JJ, Theory and Applications of Fractional Differential Equations, Elsevier(North h-Holland), Sci. Publishers, Amsterdam (2006).

      [2] Podlubny I, Fractional Differential Equations, Academic Press, New York (1999).

      [3] Sabatier J, Agrawal OP & Tenreiro Machado JA, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht (2007)

      [4] Miller KS & Ross B, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York (1993)

      [5] Fletcher, CAJ, Computational Galerkin Methods, Springer-verlag, New York, First Edition, (1984)

      [6] Hopkins TR & Wait R, “A comparison of galerkin collocation and the method of lines for PDE’sâ€, Int. J. Numer. Meth. Engin., Vol. 12 (1978), pp: 1081-1107.

      [7] Javidhi M & Golbabbai A, “Adomian decomposition method for approximating the solution of the parabolic equationsâ€, Applies Mathematical Sciences, Vol. 1, No. 5 (2007), pp: 219-225.

      [8] Keskin Y & GalipOturanc, “Reduced differential transform method for partial differential equationsâ€, Int. Journal of nonlinear sciences and numerical simulation, Vol. 10, No. 6 (2009), pp: 741-749.

      [9] Zheng-Biao Li & Ji-Huan He, “Application of the Fractional Complex Transform to Fractional Differential Equationsâ€, Nonlinear Sci.Lett.A, Vol. 2 (2011), pp:.121-126.

      [10] Rabha W Ibrahim, “Fractional complex transforms for fractional differential equationsâ€, Advances in Difference Equations, Vol. 2012 (2012), pp: 192.

      [11] Elsayed M.E.Zayed, Yasser A.Amer & Reham M.A.Shohib, “The fractional complex transformation for nonlinear fractional partial differential equations in the mathematical physicsâ€, Journal of the Association of Arab Universities for Basic and Applied Sciences, (2014) (article in press).

      [12] Saha Ray S & Sahoo, S, “A Novel Analytical Method with fractional complex transform for new exact solutions oftime-fractional fifth-order Swada-Kotera Equationâ€, Reports on Mathematical Physicss, Vol. 75 (2015), pp: 65-72.

      [13] Zheng-Biao Li, “An Extended Fractional Complex Transformâ€, International Journal of Nonlinear Sciences & Simulation, Vol. 11 (2010), pp: 335-337.

      [14] Ji-Huan He, Elagan SK & Li ZB, “Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculusâ€, Physics Letters A, Vol. 376 (2012), pp: 257-259.

      [15] Guy Jumarie, “Fractional partial differential equations ans modified Riemann-Liouville derivatives new methods for solutionâ€, J.Appl.Math.& Comp, Vol 24 (2007), pp: 31-48.

      [16] Zeng Biao Li & Ji-Juan He, “Fractional complex transform for fractional differential equationâ€, Mathematical and Computational Applications, Vol. 15 (2010), pp: 970-973.

      [17] Soufyane A & Boulmalf M, “Solution of linear and nonlinear parabolic equations by decomposition methodâ€, Journal of Applied Mathematics and Computation, Vol. 162 (2005), pp: 687-693.

  • Downloads

  • How to Cite

    R.Ramesh Rao, T. (2018). Numerical Solution of Time Fractional Parabolic Differential Equations. International Journal of Engineering & Technology, 7(4.10), 790-792. https://doi.org/10.14419/ijet.v7i4.10.26117

    Received date: 2019-01-18

    Accepted date: 2019-01-18

    Published date: 2018-10-02