Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

By Rathinasamy Sakthivel, P. Revathi, Nazim Idrisoglu Mahmudov. 2013

47 citations recorded by the source corpus.

We study the existence and asymptotic stability in pth moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces. A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. The uniqueness of the solution of the considered problem is also studied under suitable conditions. Finally, an example is given to illustrate the obtained theory.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/b745a67b65fe1838d08aa4af7b2eee56b64bd17a

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In Applied Mathematics

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Citations in the corpus

• Stochastic delay fractional evolution equations driven by fractional Brownian motion (2014, background): “[18], [19], the perturbed terms of these fractional equations are Wiener processes.”
• ASYMPTOTIC STABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY (2013, background): “[29] studied the existence and asymptotic stability in p-th moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces.”