Stability for a class of semilinear fractional stochastic integral equations

Advances in Difference Equations

Allan Fiel²  Jorge A Len⁵  David Mrquez-Carreras⁶ 

[1]Departament de Probabilitat, Lò

[2]Depto. de Control Automá

[3]gica i Estadí

[4]stica, Universitat de Barcelona, Barcelona, Catalunya

[5]tico, Cinvestav-IPN, Ciudad de Mé

[6]xico, Mexico

关键词: comparison results for fractional differential equations;    fractional Brownian motion;    Mittag-Leffler function;    stability criteria;    Young integral for Hölder continuous functions;    34A08;    60G22;    26A33;    93D99;   

DOI  :  10.1186/s13662-016-0895-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we study some stability criteria for some semilinear integral equations with a function as initial condition and with additive noise, which is a Young integral that could be a functional of fractional Brownian motion. Namely, we consider stability in the mean, asymptotic stability, stability, global stability, and Mittag-Leffler stability. To do so, we use comparison results for fractional equations and an equation (in terms of Mittag-Leffler functions) whose family of solutions includes those of the underlying equation.

【 授权许可】

CC BY