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.     

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.     

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.     

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.     

Analysis of nonlinear fractional control systems in Banach spaces

In this paper, we consider the nonlinear control systems of fractional order and its optimal controls in Banach spaces. Using the fractional calculus, Hölder’s inequality, p-mean continuity, weakly singular inequality and Leray-Schauder’s fixed point theorem with compact mapping, the sufficient condition is given for the existence and uniqueness of mild solutions for a broad class of fractional nonlinear infinite dimensional control systems. Utilizing the approximately lower semicontinuity of integral functionals and weakly compactness, we extend the existence result of optimal controls for nonlinear control systems to nonlinear fractional control systems under generally mild conditions. An example is given to illustrate the effectiveness of the results obtained.     

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.     

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.     

Existence results for fractional impulsive integrodifferential equations in Banach spaces

This paper is mainly concerned with the existence of solutions of first order nonlinear impulsive fractional integrodifferential equations in Banach spaces. The results are obtained by using fixed point principles. Further, some interesting examples are presented to illustrate the theory.     

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.     

Relaxation of nonlinear impulsive controlled systems on Banach spaces

Relaxation control for a class of semilinear impulsive controlled systems is investigated. Existence of mild solutions for semilinear impulsive controlled systems is proved. By introducing a regular countably additive measure, we convexify the original control systems and obtain the corresponding relaxed control systems. The existence of optimal relaxed controls and relaxation results is also proved.     

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.     

Collocation-approximation methods for nonlinear singular integrodifferential equations in Banach spaces

A new approximation method is proposed for the numerical evaluation of the nonlinear singular integrodifferential equations defined in Banach spaces. The collocation approximation method is therefore applied to the numerical solution of such type of nonlinear equations, by using a system of Chebyshev functions.Through the application of the collocation method is investigated the existence of solutions of the system of non-linear equations used for the approximation of the nonlinear singular integrodifferential equations, which are defined in a complete normed space, i.e., a Banach space.     

Controllability of nonlinear fractional order integrodifferential system with input delay

This paper addressed the controllability of nonlinear fractional order integrodifferential systems with input delay. Firstly, the Caputo fractional derivatives and the Mittag‐Leffler functions are employed. Thereafter, we establish a set of sufficient and necessary conditions for the controllability of the linear fractional system. Furtherly, controllability conditions of the nonlinear integrodifferential fractional order system with input delay are acquired by utilizing Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. Finally, an example is presented to demonstrate our main results.     

Controllability of integrodifferential systems with nonlocal initial conditions in Banach spaces

In this paper, we establish a sufficient condition for the controllability of a class of semilinear integrodifferential systems with nonlocal initial conditions in Banach spaces. Utilizing the measure of noncompactness, the Sadovskii fixed-point theorem, and operator semigroups, a new controllability result is presented. In particular, the compactness of the operator semigroups is dropped.     

Remark on the existence results for fractional impulsive integrodifferential equations in Banach spaces

This paper deal with the study of the existence of solutions of nonlinear fractional integrodifferential equations with impulsive conditions in Banach spaces, by means of fixed point principle. The purpose of the paper is to generalize the results of [5] and correct an error in the example included in [5].     

Nonlocal Cauchy problem for delay integrodifferential equations of Sobolev type in Banach spaces

In this paper, we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed-point theorem.     

On fractional integro-differential inclusions with state-dependent delay in Banach spaces

In this article we investigate the existence of solutions on a compact interval for the fractional integro-differential inclusions with state-dependent delay in Banach spaces when the delay is infinite. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values.     

Existence results of second-order impulsive neutral functional integrodifferential inclusions with unbounded delay in Banach spaces

This paper investigates a class of second-order impulsive neutral functional integrodifferential inclusions with unbounded delay in Banach spaces. The existence of mild solutions of these inclusions is determined by using the theory of cosine families of bounded linear operators and a recent fixed point theorem for multivalued maps due to Dhage.     

A class of degenerate fractional evolution systems in banach spaces

By using the notion of strongly (B, p)-sectorial operator and fractional differential calculus, we analyze the unique solvability of the Cauchy and Showalter problems for a class of degenerate fractional evolution systems. The results are used for the analysis of partial differential equations of fractional order with respect to the time variable.