Commenced in January 2007
Paper Count: 30831
Group Invariant Solutions of Nonlinear Time-Fractional Hyperbolic Partial Differential Equation
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129620Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 736
 K.S. Miller, B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
 A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Frcational Differential Equations, Elsevier, San Diego, 2006.
 P.J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts Math., vol. 107, 1993.
 G.W. Bluman, J.D. Cole, Similarity Methods for Differential Equations, Springer Verlag, 1974.
 L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, 1982.
 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.
 K. Al-Khaled, Numerical Solution of Time-fractional PDEs Using Sumudu Decomposition Method, Romanian Journal of Physics, vol. 60, 2015, pp. 99-110.
 Y. Zhang, Lie Symmetry Analysis to General Time-Fractional Korteweg-De Vries Equation, Fractional Differential Calculus, vol.5, 2015, pp. 125-135.
 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.
 M. Gaur, K. Singh, On Group Invariant Solutions of Fractional Order Burgers-Poisson Equation, Applied Mathematics and Computation, vol. 244, 2014, pp. 870-877.
 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.
 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.
 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).
 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.
 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.
 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.
 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.
 V.S. Kiryakova, Generalized Fractional Calculus and Applications, CRC press,1993.