Studies on existence and uniqueness results of random impulsive partial differential equations

Abstract

The subject of impulsive theory shows widespread applications and remarkable importance due to its diverse fields in aeronautics medical economics In this thesis the concept of qualitative behaviour of differential equation with random impulses are explored Further by the semigroup approach mild solutions of random impulsive neutral partial differential equations are discussed The existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis are first presented Next mild solution for random impulsive fractional damped dynamical systems using fixed point theorems is discussed Then we address the problem of mild solution for random impulsive neutral hadamard fractional differential equations Moreover we study the existence and uniqueness of mild solution for random impulsive neutral fractional q difference equations by using fixed point theorems Finally existence and uniqueness of solutions for random impulsive fractional order damped dynamical systems using mittag leffler function are discussed All the results generalize the previous results of several researchers Our approach here is based on the fixed point theorems such as Lerey Schauder Alternative Krasnoselskii fixed point theorem Banach Contraction Principle Examples and applications are provided to illustrate the theorems newline