Integro-dynamic Equations Research Articles

Weakly Perturbed Systems of Linear Integro-Dynamic Equations on Time Scales

We obtain the conditions of bifurcation from the point ε = 0 for the solutions of weakly perturbed systems of linear integro-dynamic equations on a segment [a, b] of any time scale. We propose a convergent iterative procedure for finding solutions in the form of a segment of the Laurent series.

Qualitative Results for Nonlinear Integro-Dynamic Equations via Integral Inequalities

Qualitative Results for Nonlinear Integro-Dynamic Equations via Integral Inequalities

New Fixed Point Theorem on Triple Controlled Metric Type Spaces with Applications to Volterra–Fredholm Integro-Dynamic Equations

The objective of the research article is two-fold. Firstly, we present a fixed point result in the context of triple controlled metric type spaces with a distinctive contractive condition involving the controlled functions. Secondly, we consider an initial value problem associated with a nonlinear Volterra–Fredholm integro-dynamic equation and examine the existence and uniqueness of solutions via fixed point theorem in the setting of complete triple controlled metric type spaces. Furthermore, the theorem is applied to illustrate the existence of a unique solution to an integro-dynamic equation.

Existence of solutions for nonlinear integro-dynamic equations with mixed perturbations of the second type via Krasnoselskii's fixed point theorem

Existence of solutions for nonlinear integro-dynamic equations with mixed perturbations of the second type via Krasnoselskii's fixed point theorem

Stability for neutral integro-dynamic equations with multiple functional delays on time scales

In this work, we use the Banach fixed point theorem to establish new results on the stability and asymptotic stability of the zero solution for a neutral integro-dynamic equation on time scales. The results obtained here extend those due to Yankson. We end by giving two examples to illustrate our work.

Oscillation results for second-order mixed neutral integro-dynamic equations with damping and a nonpositive neutral term on time scales

Oscillation results for second-order mixed neutral integro-dynamic equations with damping and a nonpositive neutral term on time scales

Periodicity and positivity in nonlinear neutral integro-dynamic equations with variable delay

Let T be a periodic time scale. We use Krasnoselskii's fixed point theorem for a sum of two operators to show new results on the existence of periodic and positive periodic solutions of a nonlinear neutral integro-dynamic equation with variable delay. We invert this equation to construct a sum of a contraction and a completely continuous map which is suitable for applying Krasnoselskii's theorem. The uniqueness results of this equation are studied by the contraction mapping principle.

Study of the global asymptotic stability in nonlinear neutral integro-dynamic

The main purpose of this paper is to establish the global asymptotic stability of the zero solution of a class of nonlinear neutral integro-dynamic equations in C1 rd. Global asymptotic stability results are based on the Banach fixed point theorem. The results obtained here extend the work of Huang, Zhao and Liu [19].

A solution to nonlinear Volterra integro-dynamic equations via fixed point theory

In this paper we discuss the existence and uniqueness of solutions of a certain type of nonlinear Volterra integro-dynamic equations on time scales. We investigate the problem in the setting of a complete bmetric space and apply a fixed point theorem with a contractive condition involving b-comparison function. We use the theoremto show the existence of a unique solution of some particular integro-dynamic equations.

Oscillatory and asymptotic behavior of solutions for second-order mixed nonlinear integro-dynamic equations with maxima on time scales

This paper is concerned with the oscillatory and asymptotic behavior for solutions of the following second-order mixed nonlinear integro-dynamic equations with maxima on time scales (r(t)(z?(t))?)? + ?t0 a(t,s) f(s, x(s))?s + ?n,i=1 qi(t) max s?[?i(t),?i(t)] x?(s) = 0, where z(t) = x(t) + p1(t)x(?1(t)) + p2(t)x(?2(t)), t ? [0,+?)T. The oscillatory behavior of this equation hasn?t been discussed before, also our results improve and extend some results established by Grace et al. [2] and [8].

Oscillatory Behavior of Solutions for Forced Second Order Nonlinear Functional Integro-Dynamic Equations on Time Scales

Oscillatory Behavior of Solutions for Forced Second Order Nonlinear Functional Integro-Dynamic Equations on Time Scales

Periodic Solutions of Almost Linear Volterra Integro-dynamic Equations on Periodic Time Scales

AbstractUsing Krasnoselskii’s fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. The results of this paper are new for the continuous and discrete time scales.

Oscillation Criteria for Some Higher Order Integrodynamic Equations on Timescales

We study the oscillation behavior for some higher order integrodynamic equations on timescales. We establish some new sufficient conditions guaranteeing that all solutions of theses equations are oscillatory. Some numerical examples in the continuous case are given to validate the theoretical results.

Oscillatory Behavior of Solutions of Certain Integrodynamic Equations of Second Order on Time Scales

This paper deals with the oscillatory behavior of forced second-order integrodynamic equations on time scales. The results are new for the continuous and discrete cases and can be applied to Volterra integral equation on time scale. We also provide a numerical example in the continuous case to illustrate the results.

Asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations

In this paper, we establish some new criteria on the asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations on time scales.

Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation

AbstractWe consider the system of Volterra integro-dynamic equations and obtain necessary and sufficient conditions for the uniform stability of the zero solution employing the resolvent equation coupled with the variation of parameters formula. The resolvent equation that we use for the study of stability will have to be developed since it is unknown for time scales. At the end of the paper, we furnish an example in which we deploy an appropriate Lyapunov functional. In addition to generalization, the results of this paper provides improvements for its counterparts in integro-differential and integro-difference equations which are the most important particular cases of our equation.

Retraction notice to: “Oscillation of integro-dynamic equations on time scales” [Appl. Math. Lett. 25 (12) (2012) 2286–2289

Retraction notice to: “Oscillation of integro-dynamic equations on time scales” [Appl. Math. Lett. 25 (12) (2012) 2286–2289

Asymptotic Behavior of Non-oscillatory Solutions of Second order Integro-Dynamic Equations on Time Scales

In this paper, we investigate some new criteria on the asymptotic behavior of non-oscillatory solutions of second order integro-dynamic equations on time-scales. We also provide some numerical examples to illustrate the relevance of the obtained results.

Oscillation of integro-dynamic equations on time scales

In this paper, the authors initiate the study of oscillation theory for integro-dynamic equations on time-scales. They present some new sufficient conditions guaranteeing that the oscillatory character of the forcing term is inherited by the solutions.

RETRACTED: Oscillation of integro-dynamic equations on time scales

This article has been retracted: please see Elsevier Policy on Article Withdrawal ( http://www.elsevier.com/locate/withdrawalpolicy ). This article has been retracted at the request of the Editor-in-Chief and Authors. The article was found to contain errors which will be corrected in a revised version to be submitted to Applied Mathematics Letters .