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Residual Power Series Method for Fractional Diffusion Equations

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, improved residual power series method (RPSM) is effectively implemented to find the approximate analytical solution of a time fractional diffusion equations. The proposed method is an analytic technique based on the generalized Taylor’s series formula which construct an analytical solution in the form of a convergent series. In order to illustrate the advantages and the accuracy of the RPSM, we have applied the method to two different examples. In case of first example, different cases of initial conditions are considered. Finally, the solutions of the time fractional diffusion equations are investigate through graphical representation, which interpret simplicity, accuracy and practical usefulness of the present method.
Wydawca
Rocznik
Strony
213--230
Opis fizyczny
Bibliogr. 19 poz., rys., wykr.
Twórcy
autor
  • Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, 831014 – India
autor
  • Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, 831014 – India
autor
  • School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221008, China
Bibliografia
  • [1] Podlubny I. Fractional differential equations, USA, Academic Press, New York; 1999. doi: 10.1007/s00144-010-0021-2.
  • [2] Caputo M, Mainardi F. A new dissipation model based on memory mechanism, Pure and Applied Geophysics. 1971; 91: 134-147. doi: 10.1007/BF00879562.
  • [3] Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations, Wiley, New York; 1993. ISBN-10: 0471588849, 13: 978-0471588849.
  • [4] Kilbas A, Srivastava HM, Trujillo JJ. Theory and application of fractional differential equations, Elsevier, Amsterdam; 2006. ISBN: 0444518320.
  • [5] Kumar S, Kumar A, Argyros IK. A new analysis for the Keller-Segel model of fractional order. Numerical Algorithm (2016). doi: 10.1007/s11075-016-0202-z.
  • [6] Kumar, S. A new analytical modelling for telegraph equation via Laplace transform. Appllied Mathematical Modelling. 2014; 38: 3154-3163. doi: 10.1016/j.apm.2013.11.035.
  • [7] Kumar S, Yildirim A, Khan Y, Leilei W. A fractional model of diffusion equation by using Laplace transform. Scientia Iranica. 2012; 19: 1117-1123. doi: 10.1016/j.scient.2012.06.016.
  • [8] Das S. Analytical solution of a fractional diffusion equation by variational iteration method. Computers and Mathematics with Applications. 2009; 57: 483-487. doi: 10.1016/j.camwa.2008.09.045.
  • [9] Caputo M. Linear models of dissipation whose Q is almost frequency independent-11. Geophysical Journal International. 1967; 13: 529-539. doi: 10.1111/j.1365-246X.1967.tb02303.
  • [10] Yang XJ, Machadob JAT, Srivastava HM. A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach. Appllied Mathematics and Computation. 2015; 274: 143-151. doi: 10.1016/j.amc.2015.10.072.
  • [11] Yang XJ, Srivastava HM, Cattani C. Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics. Romanian Reports in Physics. 2015; 67: 752-761.
  • [12] Yang Z, Zhao Y, Fan G. A new iteration algorithm for solving the diffusion problem in non-differentiable heat transfer. Thermal Science 2015; 19: 105-108. doi: 10.2298/TSCI15S1S05Y.
  • [13] Yang XJ, Baleanu D, Srivastava HM. Local fractional similarity solution for the diffusion equation defined on Cantor sets. Applied Mathematics Letters 2015; 47: 54-60. doi: 10.1016/j.am1.2015.02.024.
  • [14] Yan SR Local fractional Laplace series expansion method for diffusion equation arising in fractal heat transfer. Thermal Science 2015; 19: 131-135. doi: 10.2298/TSCI141010063Y.
  • [15] Yao JJ, Kumar A, Kumar S. A fractional model to describe the Brownian motion of particles and its analytical solution. Advance in Mechanical Engineering. 2015; 7: 1-11. doi: 10.1177/1687814015618874.
  • [16] Abu Arqub O. Series solution of fuzzy differential equations under strongly generalized differentiability. Journal of Advanced Research in Applied Mathematics. 2013; 5: 31-52. doi: 10.5373/jaram.1447.051912.
  • [17] Kumar S, Kumar A, Baleanu D. Two analytical methods for time-fractional nonlinear coupled Boussinesq Burgers equations arise in propagation of shallow water waves. Nonlinear Dynamic. 2016; 85: 699-715. doi; 10.1007/s11071-016-2716-2.
  • [18] Kumar A, Kumar S, Singh M. Residual power series method for fractional Sharma-Tasso-Olever equation. Communication in Numerical Analysis. 2016; 1: 1-10. doi: 10.5899/2016/cna-00235.
  • [19] Dehghan M. Application of Adomian decomposition method for two dimensional parabolic equation subject to nonstandard boundary specification. Appllied Mathematics and Computation. 2004; 157: 549-560. doi: 10.1016/j.amc.2003.08.098.
Typ dokumentu
Bibliografia
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