Controllability of fractional integrodifferential systems in Banach spaces

In this paper we study the controllability of fractional integrodifferential systems in Banach spaces. The results are obtained by using fractional calculus, semigroup theory and the fixed point theorem.     

Controllability of fractional impulsive neutral integrodifferential systems with a nonlocal Cauchy condition in Banach spaces

In this work the controllability of fractional impulsive neutral functional integrodifferential systems with a nonlocal Cauchy condition in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional powers of operators and the Banach contraction mapping theorem.     

Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces

In this paper sufficient conditions for the controllability of impulsive neutral integrodifferential systems with infinite delay are established. The results are obtained by using the Schauder fixed point theorem.     

Multivalued evolution equations with nonlocal initial conditions in Banach spaces

We prove the existence of integral solutions to the nonlocal Cauchy problem in a Banach space X, where is m-accretive and such that –A generates a compact semigroup, has nonempty, closed and convex values, and is strongly-weakly upper semicontinuous with respect to its second variable, and . The case when A depends on time is also considered.      

Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces

In this work the controllability of fractional impulsive neutral functional integrodifferential systems in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional calculus, a semigroup of operators and Krasnoselskii’s fixed point theorem.     

Controllability of nonlinear integrodifferential systems in Banach space

Sufficient conditions for controllability of nonlinear integrodifferential systems in a Banach space are established. The results are obtained using the Schauder fixed-point theorem.The work of the first and third authors was supported by CSIR, New Delhi, India.     

Existence results of semilinear differential equations with nonlocal initial conditions in Banach spaces

In this paper, we establish the existence results for semilinear differential systems with nonlocal initial conditions in Banach spaces. The approaches used are fixed point theorems combined with convex-power condensing operators. The first result obtained will be applied to a class of semilinear parabolic equations.     

Boundary controllability of integrodifferential systems in Banach spaces

Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.     

Controllability of semilinear boundary problems with nonlocal initial conditions

The main purpose of this paper is the existence of solutions and controllability for semilinear boundary problems with nonlocal initial conditions. We show that the solutions are given by a variation of constants formula which allows us to study the exact controllability for this kind of problems with control and nonlinear terms at the boundary. The included application to a size structured population equation provides a motivation for abstract results.     

Controllability of impulsive differential systems with nonlocal conditions

The paper is concerned with the controllability of impulsive functional differential equations with nonlocal conditions. Using the measure of noncompactness and Mönch fixed-point theorem, we establish some sufficient conditions for controllability. Firstly, we require the equicontinuity of evolution system, and next we only suppose that the evolution system is strongly continuous. Since we do not assume that the evolution system generates a compact semigroup, our theorems extend some analogous results of (impulsive) control systems.     

Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces

In this paper approximate and exact controllability for semilinear stochastic functional integrodifferential systems are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the theory.     

The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces

In this paper we prove the existence of solutions of certain kinds of nonlinear fractional integrodifferential equations in Banach spaces. Further, Cauchy problems with nonlocal initial conditions are discussed for the aforementioned fractional integrodifferential equations. At the end, an example is presented.     

Existence of solutions of nonlinear integrodifferential equations of sobolev type with nonlocal condition in Banach spaces

In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.     

Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions

Of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions. Under some suitable hypotheses, we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations. Moreover, an example is given to illustrate our results.     

Controllability of impulsive functional differential systems with infinite delay in Banach spaces

The paper establishes a sufficient condition for the controllability of the first-order impulsive functional differential systems with infinite delay in Banach spaces. We use Schauder’s fixed point theorem combined with a strongly continuous operator semigroup. An example is given to illustrate our results.     

A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces

We study a class of fractional delay nonlinear integrodifferential controlled systems associated with analytic semigroup in Banach spaces. Existence of α-mild solutions and optimal controls are obtained. Lastly, an example is presented to illustrate our abstract results.     

Controllability of stochastic Volterra integrodifferential systems

In this paper, sufficient conditions for the controllability of stochastic integrodifferential systems in Banach spaces are established. The results are obtained by using a fixed point theorem. An example is provided to illustrate the theory.     

Impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in Banach spaces

In this paper we deal with the existence of impulsive mild solutions for semilinear differential inclusions with nonlocal conditions, where the linear part generates an evolution system and the nonlinearity satisfies the lower Scorza-Dragoni property. Our theorems extend the existence propositions proved by Fan in 2010. An example is presented.     

Extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces

1. IntroductionIn paPer l1], Guo Da jun established the eristence of extreme solutions of initnd Vaueproblems fOr first order illtegrodmerelltial eqllations of VOlterra type in Banach spaces.Now, in this paPer, we consider the IVP for second order illtegrodifferelltial equatinns onthe infinite iliterVa R in BanaCh space E:U" = F(t, u,u', Tu), Vt E R , u(0) = xo, u'(0) = x1) (1)where xo,x1 E E,F E C(R x E x E x E,E), and(Tx)(t) = l'k(,,.).(.)d., Vt E R , (2)jok E C(fl, R ), fl…     

Controllability of nonlinear neutral evolution integrodifferential systems

Sufficient conditions for controllability of nonlinear neutral evolution integrodifferential systems in a Banach space are established. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An application to partial integrodifferential equation is given.