Asymptotic behavior of solutions to fractional stochastic multi-term\n differential equation systems involving non-permutable matrices

2021/03/13 by Arzu Ahmadova, Ahmadova, Arzu, Nazım I. Mahmudov +1
Mathematics · #34D05 #60H10 #93E03 #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2103.07690

openalex publication_date 2021/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the exact asymptotic separation rate of two distinct\nsolutions of Caputo stochastic multi-term differential equations (Caputo SMTDEs\nfor short). Our goal in this paper is to establish results on the global\nexistence and uniqueness and continuity dependence of the initial values of the\nsolutions to Caputo SMTDEs with non-permutable matrices of order \α \∈\n(\(1)/(2),1) and \β \∈ (0,1) whose coefficients satisfy a standard\nLipschitz condition. For this class of systems, we then show the asymptotic\nseparation property between two different solutions of Caputo SMTDEs with a\nmore general condition based on \λ. Also, the asymptotic separation rate\nfor the two distinct mild solutions reveals that our asymptotic results are\ngeneral.\n

Citations

• Fractional Brownian Motions, Fractional Noises and Applications
• Fractional Differential Equations
• A new technique for solving Sobolev type fractional multi-order\n evolution equations

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