Abstract

There is a type of fractional differential equation that admits asymptotically free standing oscillations (Fukunaga, M., 2019, “Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations,” ASME J. Comput. Nonlinear Dyn., 14, p. 061005). In this paper, analytical solutions to fractional differential equation for free oscillations are derived for special cases. These analytical solutions are direct evidence for asymptotically standing oscillations, while numerical solutions give indirect evidence.

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