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Publication Type : Journal Article
Publisher : Springer
Source : Computational and Applied Mathematics, 40(2021), 1-42, Springer [SCI, Impact factor:2.239, Citations: 1].
Campus : Coimbatore
School : School of Engineering
Department : Mathematics
Year : 2021
Abstract : This work investigates how we can extend the invariant subspace method to two-dimensional time-fractional non-linear PDEs. More precisely, the systematic study has been provided for constructing the various dimensions of the invariant subspaces for the two-dimensional time-fractional generalized convection-reaction-diffusion-wave equation along with the initial conditions for the first time. Additionally, the special types of the above-mentioned equation are discussed through this method separately such as reaction-diffusion-wave equation, convection-diffusion-wave equation and diffusion-wave equation. Moreover, we explain how to derive variety of exact solutions for the underlying equation along with initial conditions using the obtained invariant subspaces. Finally, we extend this method to two-dimensional time-fractional non-linear PDEs with time delay. Also, the effectiveness and applicability of the method have been illustrated through the two-dimensional time-fractional cubic non-linear convection-reaction-diffusion-wave equation with time delay. In addition, we observe that the obtained exact solutions can be viewed as the combinations of Mittag-Leffler function and polynomial, exponential and trigonometric type functions.
Cite this Research Publication : P. Prakash, K.S. Priyendhu, K.M.Anjitha, Initial value problem for the generalizedtime-fractional two-dimensional convection-reaction-diffusion-wave equations, Computational and Applied Mathematics, 40(2021), 1-42, Springer [SCI, Impact factor:2.239, Citations: 1].