20 research outputs found
Controllability of nonlinear integro-differential third order dispersion system
No full textAbstractIn this short article, sufficient condition for controllability of nonlinear dispersion system is studied. The result is obtained by using the Schaefer fixed-point theorem. This work extends the work of Chalishajar, George and Nandakumaran [D.N. Chalishajar, R.K. George, A.K. Nandakumaran, Exact controllability of the third order nonlinear dispersion equation, J. Math. Anal. Appl. 332 (2007) 1028–1044]. Usually authors assume the compactness of semigroup while studying the controllability. Here we drop this assumption and prove the controllability result
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
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
Controllability of Impulsive Partial Neutral Functional Differential Equation with Infinite Delay
No full textIn this paper, we examine sufficient condition for controllability of first order impulsive partial neutral functional differential equations. Here we do not assume that the system generates a compact semigroup, so method is applicable to a wide class of impulsive partial neutral functional differential equations in Banach spaces. Also we claim that phase space for infinite delay with impulse, considered by different authors are not correct
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
Fuzzy Solutions to Second Order Three Point Boundary Value Problem
Full text linkIn this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum of the Hausdorff distance between level sets is obtained. Then to further establish the existence, fixed point theorem for absolute retracts is used by taking consideration that space of fuzzy sets can be embedded isometrically as a cone in Banach space. Finally, an example is provided to illustrate the result
Exact Controllability of Generalized Hammerstein Type Integral Equation and Applications
No full textExact 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 Neutral Impulsive Differential Inclusions with Non-Local Conditions
No full textIn this short article, we have studied the controllability result for neutral impulsive differential inclusions with nonlocal conditions by using the fixed point theorem for condensing multi-valued map due to Martelli [1]. The system considered here follows the P.D.E involving spatial partial derivatives with α-norms
