Existence and Controllability Result for Nonlinear Neutral Evolution Integrodifferential Systems

In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in Banach spaces. The result is obtained by using the resolvent operators and fixed point analysis approach.

Optimal control of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps

In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.

Constrained controllability of nonlinear neutral fractional integrodifferential systems

In this paper,we study the complete controllability for a class of nonlinear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assigned in advance.The result is achieved using the Banach fixedpoint theorem and Schauder’s fixed-point theorem.Some numerical examples are provided to demonstrate the effectiveness of the main result.

ONE LINEAR ANALYTIC APPROXIMATION FOR STOCHASTIC INTEGRODIFFERENTIAL EQUATIONS

This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L^p-th norm, uniformly on the time interval. The convergence with probability one is also given.

GLOBAL EXISTENCE OF SOLUTION TO NONLINEAR INTEGRODIFFERENTIAL EQUATION IN A BANACH SPACE

Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.

NUMERICAL STUDY OF A NONLINEAR INTEGRODIFFERENTIAL EQUATION

In this Paper. by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations is investigated numerically. It is found that for small ∈, the result is close to that of the KdV equation, whereas the effects of larger ∈ and the initial condition are significant.

Existence Results on General Integrodifferential Evolution Equations in Banach Space

In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a sufficient condition for the existence of general integrodifferential evolution equations is established.

Existence for Second Order Semilinear Impulsive Delay Integrodifferential Equations with Nonlocal Conditions

A fixed point analysis approach is used to investigate the existence of mild solutions of second order semilinear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness condition on the cosine family of operators,we give some sufficient conditions for the existence of mild solutions of such system.Finally,an example is presented to illustrate the utility of the proposed result.The results improve some recent results.

Spectral Method for Semilinear Parabolic Integrodifferential Equations

Based on the discussion of the semidiscretization of a parabolic equation with asemilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler method in time The trapezoidal rule is adopted.for the quadrature of the memory term and the quadrature error isestimated.

Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions

In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.

Controllability results for nonlinear impulsive integrodifferential evolution systems with time-varying delays

In this paper, we study the controllability results for the nonlinear impulsive integrodifferential evolution systems with time-varying delays in Banach spaces. The sufficient conditions of exact controllability is proved under without assuming the compactness of the evolution operator. The results are obtained by using the semigroup theory and the Schafer fixed point theorem.

Bell Polynomial Approach for the Solutions of Fredholm Integro- Differential Equations with Variable Coefficients

In this article,we approximate the solution of high order linear Fredholm integro-differential equations with a variable coefficient under the initial-boundary conditions by Bell polynomials.Using collocation points and treating the solution as a linear combination of Bell polynomials,the problem is reduced to linear system of equations whose unknown variables are Bell coefficients.The solution to this algebraic system determines the approximate solution.Error estimation of approximate solution is done.Some examples are provided to illustrate the performance of the method.The numerical results are compared with the collocation method based on Legendre polynomials and the other two methods based on Taylor polynomials.It is observed that the method is better than Legendre collocation method and as accurate as the methods involving Taylor polynomials.

The Cauchy Problem for a Class of Intergrodifferential Equations

The existence, uniqueness of bounded and continuous solutions of a class of integrodifferential equations and some estimates of solutions are established. Applying these results to integrodifferential systems with a small parameter ε>0 , we obtain, in particular, some estimates of solutions uniform in ε.

EXTRAPOLATION AND DEFECT CORRECTION FOR DIFFUSION EQUATIONS WITH BOUNDARY INTEGRAL CONDITIONS

In this paper we study the higher accuracy methods - the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of the parabolic equations with boundary integral conditions. The global extrapolation and the correction approximations, rather than the pointwise extrapolation results, are derived.

Mild Solutions of Fractional Semilinear Integro-Differential Equations on an Unbounded Interval

In this paper, we study the existence of mild solutions for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. The arguments are based on the Schauder fixed point theorem.

SELFADJOINT EXTENSIONS OF VOLTERRA STIELTJES INTEGRODIFFERENTIAL OPERATORS

In this paper, we study operators generated by Volterra-Stieltjes integrodifferential expressions. The selfadjoint boundary conditions are obtained in both regular and limit circle cases. The complete description of selfadjoint extensions are given.

PBVP of Integrodifferential Equations with Carathéodory Functions

We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.

METHODS FOR IMPROVING APPROXIMATE ACCURACY FOR HYPERBOLIC INTEGRODIFFERENTIAL EQUATIONS

In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolicintegrodifferential equations. The global extrapolation and the correction approximationsof third order, rather than the pointwise extrapolation results, are derived.

Controllability of impulsive second-order nonlinear systems with nonlocal conditions in Banach spaces

In this paper,we are concerned with the controllability of damped second-order integrodifferential systems with impulses.Further the result is extended to study the controllability of nonlinear neutral systems with nonlocal conditions.The fixed point analysis approach is adopted in investigation.Sufficient conditions are formulated with a noncompact condition on the cosine family of operators.The results are obtained using the Banach fixed point theorem.An example is presented to illustrate the results.

UNIQUE EXISTENCE OF PERIODIC SOLUTIONS OF NEUTRAL VOLTERRA INTEGRODIFFERENTIAL EQUATIONS

This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.