Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations

Abstract

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.

Keywords:

• Analytic α-resolvent operator
• fixed point
• fractional impulsive neutral stochastic functional integro-differential equations
• infinite delay
• optimal solutions

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 34A37
• 60H10
• 34G25
• 26A33
• 93E20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11461019) and the President Fund of Scientific Research Innovation and Application of Hexi University (xz2013-10).