Lebesgue regularity for differential difference equationswith fractional damping
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TitleLebesgue regularity for differential difference equationswith fractional damping
We provide necessary and sufficient conditions for the existence and unique-ness of solutions belonging to the vector-valued space of sequences �(Z, X) forequations that can be modeled in the formΔu(n)+Δu(n)=Au( ... [+]
We provide necessary and sufficient conditions for the existence and unique-ness of solutions belonging to the vector-valued space of sequences �(Z, X) forequations that can be modeled in the formΔu(n)+Δu(n)=Au(n)+G(u)(n)+ (n), n ∈ Z,,>0,≥0,where X is a Banach space, ∈ �(Z, X), A is a closed linear operatorwith domain D(A) defined on X,andG is a nonlinear function. The oper-ator Δdenotes the fractional difference operator of order >0inthesense of Grünwald-Letnikov. Our class of models includes the discrete timeKlein-Gordon, telegraph, and Basset equations, among other differential differ-ence equations of interest. We prove a simple criterion that shows the existenceof solutions assuming that f is small and that G is a nonlinear term. [-]
Copyright © 2018 John Wiley & Sons, Ltd. "This is the pre-peer reviewed version of the following article: Lizama, Carlos, Murillo-Arcila, Marina and Leal, Claudio. "Lebesgue regularity for differential difference equations with fractional damping". Mathematical Methods in the Applied Sciences, 41 (2018): 2535-2545, which has been published in final form at https://doi.org/10.1002/mma.4757. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions."
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