# STABILITY IN THE α-NORM FOR SOME STOCHASTIC PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

• Accepted : 2018.05.30
• Published : 2019.01.01
• 17 3

#### Abstract

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.

#### Keywords

analytic resolvent operators;fractional power;stochastic partial functional integrodifferential equations;Wiener process;Picard iteration;mild solution;exponential stability