Abstract stochastic integrodifferential delay equations

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Stability and Boundedness of Stochastic Volterra Integrodifferential Equations with Infinite Delay

Wemake the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov-Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and ...

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

Nonlocal Problems for Delay Integrodifferential Equations in Banach Spaces

In this paper we study the existence of mild solutions for a class of first-order delay integrodifferential equations with nonlocal condition in a Banach space. The results are established by the application of the theory of resolvent operators, the contraction mapping principle and the Schaefer theorem. An example is presented in the end to show the applications of the obtained results. Mathem...