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Group invariant solution of some time fractional evolution equations

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Języki publikacji
EN
Abstrakty
EN
In this paper, we consider some classes of a system of nonlinear fractional differential equations (FDEs) arising in some important physical phenomena. Using symmetry group of transformations, the given systems of fractional partial differential equations (FPDEs) are reduced to systems of fractional ordinary differential equations (FODEs). Further, using the group invariant condition, we solve the reduced systems of FODEs and exact solutions of the given equations are constructed. Finally, the physical significance of the solutions are investigated graphically based on the exact solutions in order to highlight the importance of the study.
Rocznik
Strony
35--46
Opis fizyczny
Bibliogr. 23 poz., rys.
Twórcy
autor
  • Department of Mathematics, SRM Institute of Science and Technology Chennai, India
autor
  • Department of Mathematics, SRM Institute of Science and Technology Chennai, India
Bibliografia
  • [1] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier Science B.V.
  • [2] Hilfer, R. (2000). Applications of Fractional Calculus in Physics. Singapore: World Scientific.
  • [3] Xu, X.Y., & Tan, W.C. (2006). Intermediate processes and critical phenomena: theory, methods and progress of fractional operators and their applications to modern mechanics. Science in China Series G, 49, 257-272.
  • [4] El-Sayed, A.M.A., & Gaber, M. (2006). The Adomian decomposition method for solving partial differential equations of fractal order in finite domains. Phys Lett A, 359, 175-182.
  • [5] Wang, H., & Du, N., (2014). Fast alternating-direction finite difference methods for threedimensional space-fractional diffusion equations. Journal of Computational Physics, 258, 305-318.
  • [6] Zhang, Y.N., Sun, Z.Z., & Liao, H.L. (2014). Finite difference methods for the time fractional diffusion equation on non-uniform meshes. Journal of Computational Physics, 265, 195-210.
  • [7] Liu, J., & Hou, G. (2011). Numerical solutions of the space-and time-fractional coupled Burgers equations by generalized differential transform method. Applied Mathematics and Computation, 217, 7001-7008.
  • [8] Wu, G.C., Shi, Y.G., & Wu, K.T. (2011). Adomian decomposition method and non-analytical solutions of fractional differential equations. Romanian Journal of Physics, 56, 873-880.
  • [9] Bekir, A., Askoy, E., & Cevikel, A.C. (2015). Exact solutions of nonlinear time fractional differential equations by sub-equation method. Mathematical Methods in the Applied Sciences, 38, 2779-2784.
  • [10] Olver, P.J. (1986). Applications of Lie Groups to Differential Equations. New York: Springer.
  • [11] Bluman, G.W., & Anco, S.C. (2002). Symmetries and Integration Methods for Differantial Equations. New York: Springer-Verlag.
  • [12] Nayak, S., & Chakraverty, S. (2018). Interval Finite Element Method with MATLAB. Academic Press.
  • [13] Chakraverty, S., & Nayak, S. (2017). Neutron Diffusion: Concepts and Uncertainty Analysis for Engineers and Scientists. Florida: CRC Press.
  • [14] Buckwar, E., & Luchko, Y. (1998). Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Journal of Mathematical Analysis and Applications, 227, 81-97.
  • [15] Hu, J., Ye, Y., Shen, S., & Zhang, J. (2014). Lie symmetry analysis of the time fractional KdVtype equation. Applied Mathematics and Computation, 233, 439-444.
  • [16] Gazizov, R.K., Kasatkin, A.A., & Lukashchuk, S.Y. (2007). Symmetry properties of fractional diffusion equations. Physica Scripta, 136, 014016.
  • [17] Liu, H.Z. (2013). Complete group classifications and symmetry reductions of the fractional fifthorder KdV types of equations. Studies in Applied Mathematics, 131, 317-330.
  • [18] Yaşar, E., & Giresunlu, ˙I, B. (2015). Lie symmetry reductions, exact solutions and conservation laws of the third order variant Boussinesq system. Applicable Analysis, 128, 252-255.
  • [19] Podlubny, I. (1999). Fractional Differential Equations. San Diego: Academic Press.
  • [20] Oldham, K.B., & Spanier, J. (2006). The Fractional Calculus. New York: Dover Publications.
  • [21] Ali, K.K., Raslan, K.R., & EL-Danaf, T.S. (2015). Non-polynomial Spline Method for Solving Coupled Burgers’ Equations. Computational Methods for Differential Equations, 3, 218-230.
  • [22] Costa, F.S., Marão, J.A., Soares, J.C., & Oliveira, E.C. (2015). Similarity solution to fractional nonlinear space-time diffusion-wave equation. Journal of Mathematical Physics, 56, 033507.
  • [23] Geng, X., & Li, R. (2015). Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions. Annals of Physics, 361, 215-225.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b6139184-048f-46f4-a411-b8337f7173f9
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