Kucche, K.D. and Dhakne, M. B. (2014) Sobolev-Type Volterra-Fredholm Functional Integrodifferential Equations in Banach Spaces. Boletim da Sociedade Paranaense de Matemática, 32, 237-255.

has been cited by the following article:

• TITLE: A Study on Stochastic Differential Equation Using Fractional Power of Operator in the Semigroup Theory

  AUTHORS: Emmanuel Hagenimana, Charline Uwilingiyimana, Umuraza Clarisse

  KEYWORDS: Stochastic, Impulsive Stochastic, Neutral Functional, Mild Solution, Wiener Process, Brownian Motion, Banach Space

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.6, June 29, 2023

  ABSTRACT: Stochastic differential equation (SDE) is an ordinary differential equation with a stochastic process that can model the unpredictable real-life behavior of any continuous systems. It is the combination of differential equations, probability theory, and stochastic processes. Stochastic differential equations arise in modeling a variety of random dynamic phenomena in physical, biological and social process. The SDE theory is traditionally used in physical science and financial mathematics. Recently, more researchers have been conducted in the application of SDE theory to various areas of engineering. This dissertation is mainly concerned with the existence of mild solutions for impulsive neutral stochastic differential equations with nonlocal conditions in Hilbert spaces. The results are obtained by using fractional powers of operator in the semigroup theory and Sadovskii fixed point theorem.