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Idea of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs

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  • Rui, Weiguo

Abstract

In this paper, inspired by the idea of invariant subspace method and combined with elementary integral method, we introduced a novel approach for investigating exact solutions of a time-fractional nonlinear partial differential equation (NPDE). Based on hypothetical structure of solution of separated variable, a time-fractional NPDE defined by time and space variables can be reduced to a nonlinear ordinary differential equation (NODE) or NODEs defined by space variable alone, and then using the elementary integral method to solve the NODE or NODEs, different kinds of exact solutions of a time-fractional NPDE are obtained finally. As examples, the time-fractional Hunter–Saxton equation and time-fractional Li–Olver equation were studied. Different kinds of exact solutions of these equations were obtained and their dynamical properties were illustrated.

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  • Rui, Weiguo, 2018. "Idea of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 158-171.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:158-171
    DOI: 10.1016/j.amc.2018.07.033
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    1. Metzler, Ralf & Glöckle, Walter G. & Nonnenmacher, Theo F., 1994. "Fractional model equation for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(1), pages 13-24.
    2. Anh, V. V. & Leonenko, N. N., 2000. "Scaling laws for fractional diffusion-wave equations with singular data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 239-252, July.
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    Cited by:

    1. Rui, Weiguo & Yang, Xinsong & Chen, Fen, 2022. "Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).

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