Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30135
Group Invariant Solutions of Nonlinear Time-Fractional Hyperbolic Partial Differential Equation

Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

Abstract:

In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129620

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 670

References:


[1] K.S. Miller, B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
[2] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Frcational Differential Equations, Elsevier, San Diego, 2006.
[3] P.J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts Math., vol. 107, 1993.
[4] G.W. Bluman, J.D. Cole, Similarity Methods for Differential Equations, Springer Verlag, 1974.
[5] L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, 1982.
[6] Q. Huang, R. Zhdanov, Symmetries and Exact Solutions of the Time Fractional Harry-Dym Equation with Riemann-Liouville Derivative, Physica A, vol. 409, 2014, pp. 110-118.
[7] K. Al-Khaled, Numerical Solution of Time-fractional PDEs Using Sumudu Decomposition Method, Romanian Journal of Physics, vol. 60, 2015, pp. 99-110.
[8] Y. Zhang, Lie Symmetry Analysis to General Time-Fractional Korteweg-De Vries Equation, Fractional Differential Calculus, vol.5, 2015, pp. 125-135.
[9] V.D. Djordjevic, T.M. Atanackovic, Similarity Solutions to Nonlinear Heat Conduction and Burgers/Korteweg-De Vries Fractional Equations, Journal of Computational Applied Mathematics, vol. 222, 2008, pp. 701-714.
[10] M. Gaur, K. Singh, On Group Invariant Solutions of Fractional Order Burgers-Poisson Equation, Applied Mathematics and Computation, vol. 244, 2014, pp. 870-877.
[11] H. Liu, J. Li, Q. Zhang, Lie Symmetry Analysis and Exact Explicit Solutions for General Burgers Equations, Journal of Computational Applied Mathematics, vol. 228, 2009, pp. 1-9.
[12] H. Liu, Complete Group Classifications and Symmetry Reductions of the Fractional fifth-order KdV Types of Equations, Studies in Applied Mathematics, vol. 131, 2013, pp. 317-330.
[13] A. Bansal, R.K. Gupta, Lie point Symmetries and Similarity Solutions of the Time-Dependent Coefficients Calogero-Degasperis Equation, Physica Scripta, vol. 86, 2012, pp. 035005 (11 pages).
[14] A. Bansal, R.K. Gupta, Modified (G'/G)-Expansion Method for Finding Exact Wave Solutions of Klein-Gordon-Schrodinger Equation, Mathematical Methods in the Applied Sciences, vol. 35, 2012, pp. 1175-1187.
[15] R.K. Gupta, A. Bansal, Painleve Analysis, Lie Symmetries and Invariant Solutions of potential Kadomstev Petviashvili Equation with Time Dependent Coefficients, Applied Mathematics and Computation, vol. 219, 2013, pp. 5290-5302.
[16] R. Kumar, R.K. Gupta, S.S. Bhatia, Lie Symmetry Analysis and Exact Solutions for Variable Coefficients Generalised Kuramoto-Sivashinky Equation, Romanian Reports in Physics, vol. 66, 2014, pp. 923-928.
[17] M. Pandey, Lie Symmetries and Exact Solutions of Shallow Water Equations with Variable Bottom, Internation Journal of Nonlinear Science and Numerical Simulation, vol. 16, 2015, pp. 337-342.
[18] V.S. Kiryakova, Generalized Fractional Calculus and Applications, CRC press,1993.