Approximate Controllability of Fractional Sobolev Type Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion

Salah H. Abid^1, , Sameer Q. Hasan¹ and Uday J. Quaez¹

¹Mathematics department, Education College, Al-Mustansiriya University, Baghdad, Iraq

Cite this paper:
Salah H. Abid, Sameer Q. Hasan and Uday J. Quaez. Approximate Controllability of Fractional Sobolev Type Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion. Journal of Mathematical Sciences and Applications. 2015; 3(1):3-11. doi: 10.12691/jmsa-3-1-2

Abstract

In this paper, the approximate controllability of nonlinear Fractional Sobolev type with order Caputo stochastic differential equations driven by mixed fractional Brownian motion in a real separable Hilbert spaces has been studied by using contraction mapping principle, fixed point theorem, stochastic analysis theory, fractional calculus and some sufficient conditions.

Keywords:
approximate controllability mixed fractional brownian motion fixed point contraction principle stochastic differential equations mild solution control function

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