Nonlinear fractional dynamics with Kicks

V.E. Tarasov

Chaos, Solitons & Fractals, 2021, vol. 151, issue C

Abstract: A new type of nonlinear fractional dynamics (NFD) with kicks in the form of discrete maps with Erdelyi-Kober nonlocality in time is described. These maps are derived from nonlinear fractional differential equations with operators of the Erdelyi-Kober type and periodic sequence of kicks. Exact solutions of these nonlinear equations are obtained. Using these solutions, the new type of nonlinear discrete maps with the Erdelyi-Kober nonlocality in time is derived without any approximations. As examples, the proposed maps with Erdelyi-Kober nonlocality in time are suggested for order parameter lying in the intervals (0,1) and (1,2). The proposed new discrete fractional dynamics does not depend on the period of periodic kicks at zero initial conditions.

Keywords: Nonlinear dynamics; Fractional dynamics; Discrete maps with memory; Erdelyi-Kober fractional operators (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006135

DOI: 10.1016/j.chaos.2021.111259

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