Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions

Abstract

This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. Furthermore, the uniqueness of PC-mild solutions is proved in the case of the noncompact resolvent operator.

Study of Non-Linear Impulsive Neutral Fuzzy Delay Differential Equations with Non-Local Conditions

“…Neutral differential equations are utilized in several areas of mathematical practice due to their wide range of applications. Electricity, heat conduction in material with memory, growth problems, drug administration in the human body, balancing a pencil on a finger tip, and simulation of a jumping ball are some domains where we apply fuzzy differential equations [22][23][24][25]. They have obtained a lot of attention in recent years.…”

“…They worked on the fundamental theory of existence and uniqueness, as well as attributes of the solution operator and also worked for stability. Many researchers have contributed to the field of neutral functional differential equations [24,[30][31][32][33][34][35]. Benchohra [36] investigated neutral functional differential equations and integro differential equations augmentation in Banach spaces for the non-local Cauchy problems.…”