1,720,967 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
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
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
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 text(SI14-12) Some Novel Fractional Discrete Inequalities of Gronwall-Bellman Type and Their Applications to Fractional Difference Equations
Full text linkIn this study, we develop multiple power nonlinear generalizations of Gronwall-Bellman type fractional discrete inequalities and fractional sum inequalities through combining functions with powered unknown functions.We have employed technique of reducing power non-linearity into linearity to furnish these refinements. These novel findings present a broader framework for dealing with wider range of nonlinear fractional difference equations and fractional sum-difference equations. The utilization of these inequalities enables to study certain crucial classes of fractional difference equations that arise in the realm of fractional difference calculus, both quantitatively and qualitatively. Several illustrations are provided to examine the boundedness of initial value problems of fractional difference equations, demonstrating the reliability and effectiveness of our findings
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
Controllability of Second-Order Semi-Linear Neutral Impulsive Differential Inclusions on Unbounded Domain with Infinite Delay in Banach Spaces
No full textIn this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators
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
x(t) = ∫t0 h(t, s)u(s)ds + ∫t0k(t, s, x)ƒ(s, x(s))ds, 0 ≤ t ≤ T < ∞,
where, the state x(t) lies in a Hilbert space H and control u(t) lies another Hilbert space V for each time t ∈ I = [0, T], T > 0. We establish the controllability result under suitable assumptions on h, k and ƒ using the monotone operator theory.Mathematic
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