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Almost periodic dynamics in a new class of impulsive reaction-diffusion neural networks with fractional-like derivatives. (English) Zbl 1498.92018

Summary: This paper introduces a new class of reaction-diffusion neural networks with impulses and recently defined fractional-like derivatives. Sufficient conditions for the existence-uniqueness of almost periodic solutions are proposed by constructing suitable Lyapunov-like functions. Our results are new and contribute to the development of the knowledge on impulsive fractional-like evolution models. Finally, as an example a fractional-like generalization of a reaction-diffusion model in epidemiology that simulates the hepatitis B virus (HBV) infection with spatial dependence is considered.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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