Stochastic impulsive fractional differential evolution equations with infinite delay

2015/08/07 by Zhao Shufen, Shufen, Zhao, Song Minghui +1
Mathematics · #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #math.DS

paper · pdf · doi:10.48550/arxiv.1508.01592

arxiv created 2015/08/07 · openalex publication_date 2015/08/07 · arxiv updated 2015/08/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate a class of stochastic impulsive fractional differential evolution equations with infinite delay in Banach space. Firstly sufficient conditions of the existence and uniqueness of the mild solution for this type of equations are derived by means of the successive approximation. Then we use the Bihari's inequality to get the stability in mean square of the mild solution. Finally an example is presented to illustrate the results.

Citations

• Basic theory of fractional differential equations

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