Semi-dynamical systems generated by autonomous Caputo fractional differential equations

2019/05/22 by Thai Son Doan, Peter E. Kloeden, Doan, T. S. +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1905.09159

openalex publication_date 2019/05/22 · openalex created_date 2019/05/29 · openalex updated_date 2026/07/28

Abstract

An autonomous Caputo fractional differential equation of order α∈(0,1) in ℝ^d whose vector field satisfies a global Lipschitz condition is shown to generate a semi-dynamical system in the function space \mathfrakC of continuous functions f:\R⁺→ \R^d with the topology uniform convergence on compact subsets. This contrasts with a recent result of Cong & Tuan \citecong, which showed that such equations do not, in general, generate a dynamical system on the space ℝ^d.

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