Fractional infinite time-delay evolution equations with non-instantaneous impulsive

This dissertation is regarded to investigate the system of infinite time-delay and non-instantaneous impulsive to fractional evolution equations containing an infinitesimal generator operator. It turns out that its mild solution is existed and is unique. Our model is built using a fractional Caputo approach of order lies between 1 and 2. To get the mild solution, the families associated with cosine and sine which are linear strongly continuous bounded operators, are provided. It is common to use Krasnoselskii's theorem and the Banach contraction mapping principle to prove the existence and uniqueness of the mild solution. To confirm that our results are applicable, an illustrative example is introduced

Total Controllability for a Class of Fractional Hybrid Neutral Evolution Equations with Non-Instantaneous Impulses

This study demonstrates the total control of a class of hybrid neutral fractional evolution equations with non-instantaneous impulses and non-local conditions. The boundary value problem with non-local conditions is created using the Caputo fractional derivative of order 1α≤2. In order to create novel, strongly continuous associated operators, the infinitesimal generator of the sine and cosine families is examined. Additionally, two approaches are used to discuss the solution’s total controllability. A compact strategy based on the non-linear Leray–Schauder alternative theorem is one of them. In contrast, a measure of a non-compactness technique is implemented using the Sadovskii fixed point theorem with the Kuratowski measure of non-compactness. These conclusions are applied using simulation findings for the non-homogeneous fractional wave equation