1,720,963 research outputs found
Total Controllability of the Second Order Semi-Linear Differential Equation with Infinite Delay and Non-Instantaneous Impulses
No full textIn this manuscript, a stronger concept of exact controllability called Total Controllability has been introduced. Sufficient conditions have been established for the total controllability of the proposed problem. The proposed control problem is a second-order semi-linear differential equation with infinite delay and non-instantaneous impulses. The tools for study include the strongly continuous cosine family and Sadovskii’s fixed point theorem. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. In addition, the total controllability of an integrodifferential problem has been investigated. Finally, an example is provided to illustrate the analytical findings
Trajectory Controllability of Nonlinear Integro-Differential System: An Analytical and a Numerical Estimations
No full textA stronger concept of complete (exact) controllability which we call Trajectory Controllability is introduced in this paper. We study the Trajectory Controllability of an abstract nonlinear integro-differential system in the finite and infinite dimensional space setting. We will then discuss how approximations to these problems can be found computationally using finite difference methods and optimization. Examples will be presented in one, two and three dimensions
Chikungunya Transmission of Mathematical Model Using the Fractional Derivative
No full textIn this study, a mathematical model that may depict the dynamic transmission of the Chikungunya virus within a specific population has been examined. Various differential operators were considered, ranging from classical to nonlocal operators. We added a stochastic component to each instance and used the Lipschitz and linear growth criteria to illustrate the existence and uniqueness of the solutions. The most recent numerical method with Newton polynomial (are related symmetrical) interpolations was used to solve each problem numerically using MATLAB. There are some presented numerical simulations which are compared with the Lipschitz and linear growth properties. This new research work emphasizes how the Chikungunya virus model is formulated using fractional ODEs
Exact controllability of generalized Hammerstein type integral equation and applications
No full textIn this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation where, the state lies in a Hilbert space and control lies another Hilbert space for each time , greater than 0. We establish the controllability result under suitable assumptions on and using the monotone operator theory
Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay
No full textThe functional abstract second order impulsive differential equation with state dependent delay is studied in this paper. First, we consider a second order system and use a control to determine the controllability result. Then, using Sadovskii’s fixed point theorem, we get sufficient conditions for the controllability of the proposed system in a Banach space. The major goal of this study is to demonstrate the controllability of an abstract second-order impulsive differential system with a state dependent delay mechanism. The wellposed condition is then defined. Next, we studied whether the defined problem is wellposed. Finally, we apply our results to examine the controllability of the second order state dependent delay impulsive equation
CONTROLLABILITY OF SECOND ORDER SEMI-LINEAR NEUTRAL IMPULSIVE DIFFERENTIAL INCLUSIONS ON UNBOUNDED DOMAIN WITH INFINITE DELAY IN BANACH SPACES
No full textApproximate controllability of abstract impulsive fractional neutral evolution equations with infinite delay in Banach spaces
No full textIn this article, we study the approximate controllability of impulsive
abstract fractional neutral evolution equations in Banach spaces.
The main results are obtained by using Krasnoselkii's fixed point theorem,
fractional calculus and methods of controllability theory. An application
is provided to illustrate the theory. Here we have provided new definition
of phase space for the impulsive and infinite delay term. Our result is
new for the approximate controllability with infinite delay in Hilbert space
Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces
No full textPhilos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms
No full textThe motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the integral averaging technique. The established criteria improve, simplify and complement results that have been published recently in the literature. An example is also given to demonstrate the applicability of the obtained conditions
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