Existence and controllability of fractional stochastic neutral functional integro-differential systems with state-dependent delay in Fréchet spaces

Volume 9, Issue 2, pp 603--616 http://dx.doi.org/10.22436/jnsa.009.02.24

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Authors

Zuomao Yan - Department of Mathematics, Hexi University, Zhangye, Gansu 734000, P. R. China. Fangxia Lu - Department of Mathematics, Hexi University, Zhangye, Gansu 734000, P. R. China.

Abstract

This paper investigates the existence and uniqueness of solutions of mild solutions for a fractional stochastic neutral functional integro-differential equation with state-dependent delay in Fréchet spaces. The main techniques rely on the fractional calculus, properties of characteristic solution operators and fixed point theorems. Since we do not assume the characteristic solution operators are compact, our theorems guarantee the effectiveness of controllability results in the infinite dimensional spaces.

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Keywords

• Fractional neutral stochastic integro-differential equations
• fractional derivatives and integrals
• state-dependent delay
• solution operator
• fixed point theorem.

MSC

•  34A60
•  34F05
•  26A33
•  93B05

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