Integrodifferential Systems In Banach Spaces Research Articles

On the existence and stability of Caputo Volterra-Fredholm systems

In this paper, we discuss several problems related to the neutral fractional Volterra-Fredholm integro-differential systems in Banach spaces. Existence of the Schaefer's fixed point and Ulam-Hyers-Rassias stability properties for the fixed point problem will be discussed. Some results are presented, under appropriate conditions, and some open questions are pointed out. Our results extend recent results given for \(\psi\)-fractional derivative.

Controllability results for fractional integrodifferential systems in Banach spaces

In this paper, we study the controllability of fractional non-linear evolution integrodifferential system in Banach spaces. Further quasilinear and neutral evolution systems are discussed. The results are obtained by using fractional calculus and a fixed point principle.

Existence and Controllability Results for Fractional Impulsive Integrodifferential Systems in Banach Spaces

We firstly study the existence of PC-mild solutions for impulsive fractional semilinear integrodifferential equations and then present controllability results for fractional impulsive integrodifferential systems in Banach spaces. The method we adopt is based on fixed point theorem, semigroup theory, and generalized Bellman inequality. The results obtained in this paper improve and extend some known results. At last, an example is presented to demonstrate the applications of our main results.

On controllability of fractional impulsive neutral infinite delay evolution integrodifferential systems in Banach spaces

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

Controllability of nonlocal impulsive quasi-linear integrodifferential systems in Banach spaces

In this paper a set of sufficient conditions is established for the controllability of quasilinear integrodifferential systems with nonlocal and impulsive conditions in Banach spaces. The results are obtained by using evolution operator and semigroup theory. Examples are provided to illustrate the theory.

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 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.

A comment on the papers “A study on controllability of semilinear integrodifferential systems in banach spaces” and “controllability of neutral functional integrodifferential systems in banach spaces”

A comment on the papers “A study on controllability of semilinear integrodifferential systems in banach spaces” and “controllability of neutral functional integrodifferential systems in banach spaces”

Controllability of second-order integrodifferential evolution systems in Banach spaces

In this paper, we study the controllability of second-order nonlinear integrodifferential systems in Banach spaces. Further, we derive a set of sufficient conditions for the controllability of second-order nonlinear integrodifferential evolution systems in Banach spaces. The results are established by using the theory of strongly continuous cosine families of bounded linear operators and the Schaefer fixed-point theorem.

Existence and controllability result for semilinear evolution integrodifferential systems

This paper focuses on existence and controllability results of nonautonomous semilinear evolution integrodifferential systems in Banach spaces. Without imposing severe compactness condition on the resolvent operators, we obtain sufficient conditions for the existence and controllability results by using a fixed-point analysis approach. Finally, we apply these to a control system governed by distributed parameter systems.

Existence of solutions and controllability ofnonlinear integrodifferential systems in Banach spaces

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed‐point theorem. Examples are provided to illustrate the theory.

Boundary controllability of Sobolev-type abstract nonlinear integrodifferential systems

Sufficient conditions are established for boundary controllability of various classes of Sobolev-type nonlinear systems including integrodifferential systems in Banach spaces. The results are obtained using the strongly continuous semigroup of operators and the Banach contraction principle. Examples are provided to illustrate the theory.

Controllability of Nonlinear Systems in Banach Spaces: A Survey

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integro-differential systems in abstract spaces.

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.

Local Controllability of Quasilinear Integrodifferential Evolution Systems in Banach Spaces

Sufficient conditions for local controllability of quasilinear integrodifferential systems in Banach spaces are established. The results are obtained by using the analytic semigroup theory and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

Controllability of Functional Semilinear Integrodifferential Systems in Banach Spaces

Sufficient conditions for controllability of functional semilinear integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.

Controllability of integrodifferential systems in Banach spaces

Sufficient conditions for controllability of integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem. An example is provided to illustrate the theory.

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 neutral functional integrodifferential systems in Banach spaces

Sufficient conditions for controllability of neutral functional integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem. An example is provided to illustrate the theory.

Controllability of Sobolev-type semilinear integrodifferential systems in Banach spaces

Sufficient conditions for controllability of Sobolev-type semilinear integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.