Well-Posedness and stability of time-dependent impulsive neutral stochastic partial integrodierential equations with fractional Brownian motion and Poisson jumps

Ramkumar Kasinathan, Ravikumar Kasinathan, Elsayed M Elsayed

Abstract


In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependentimpulsive neutral stochastic partial integrodierential equations with fractional Brownian motionand Poisson jumps. The existence of mild solutions for the equations are discussed by means ofsemigroup theory and theory of resolvent operator. Next, certain sucient conditions and resultsare obtained by using the method of successive approximation and Bihari's inequality. Finally, anexample is provided to illustrate our results.

Keywords


Resolvent operator, Stochastic partial differential equations, Poisson jumps, Fractional Brownian motion, Successive approximation, Bihari’s inequality.

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