New Controllability Results of Fractional Nonlocal Semilinear Evolution Systems with Finite Delay

Abstract

In the present paper, sufficient conditions ensuring the complete controllability for a class of semilinear fractional nonlocal evolution systems with finite delay in Banach spaces are derived. The new results are obtained under a weaker definition of complete controllability we introduced, and then the Lipschitz continuity and other growth conditions for the nonlinearity and nonlocal item are not required in comparison with the existing literatures. In addition, an appropriate complete space and a corresponding time delay item are introduced to conquer the difficulties caused by time delay. Our main tools are properties of resolvent operators, theory of measure of noncompactness, and Mönch fixed point theorem.

A Portfolio Selection Model Based on the Interval Number

“…Model (19) presents the acceptable solution of the portfolio model based on the acceptability. e upper and lower limits of the portfolio are given as h � 0.3, 0.4, 0.2, 0.5, 0.3 { } and l � 0.01, 0, 03, 0.01, 0.01, 0 { }, respectively, and Tables 4 and 5, respectively, show the acceptable solution of model (20) and the risk of the portfolio for different μswhen α � 0.1 and α � 0.2.…”

“…Uncertainty exists everywhere, and scholars use various methods to study it [15][16][17][18][19][20][21]. Traditional portfolio theory uses probability theory to analyze the uncertainty in the financial market.…”

Controllability of Impulsive ψ-Caputo Fractional Evolution Equations with Nonlocal Conditions

“…Fractional systems have gained considerable popularity and importance due to their wide range of applications in many mathematical, physical, and engineering disciplines such as the chaotic synchronization system [1], solutions of differential systems [2][3][4], impulsive problems [5,6], quantum theory [7], diffusion phenomena [8][9][10], delay problems [11,12], systems of thermoelasticity [13,14], etc. It turns out that fractional calculus can provide a more vivid and accurate description of many practical problems than integral ones.…”

New Results on Controllability for a Class of Fractional Integrodifferential Dynamical Systems with Delay in Banach Spaces

“…Hence, if we intend to accurately describe the evolution systems, we must consider the effect of time delay. With the development of the applications for fractional calculus, research into the controllability of fractional dynamical systems with delay is increasingly extensive [20][21][22][23][24][25].…”