148 research outputs found
CONTROLLABILITY OF FRACTIONAL INTEGRODIFFERENTIAL SYSTEMS VIA SEMIGROUP THEORY IN BANACH SPACES
This paper focuses on controllability results of fractional integrodifferential systems in Banach spaces. We obtain sufficient conditions for the controllability results by using fractional calculus, semi-group theory and the fixed point theorem
Controllability Problem of Fractional Neutral Systems: A Survey
The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems
On the approximate controllability of some semilinear partial functional integrodifferential equations with unbonded delay
This work concerns the study of the approximate controllability for some nonlinear partial functional integrodifferential equation with infinite delay arising in the modelling of materials with memory, in the framework of Hilbert spaces. We give sufficient conditions that ensure the approximate controllability of the system by supposing that its linear undelayed is part approximately controllable, admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator. An example of applications is given for illustration
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
Relative Controllability of Fractional Integrodifferential Systems in Banach Spaces with Distributed Delays in the Control
In this work, Fractional Integro-differential Systems in Banach Spaces with Distributed Delays is presented for controllability analysis. Necessary and Sufficient Conditions for the system to be relatively controllable are established. The Set Functions upon which our results hinged were extracted. Uses were made of: Unsymmetric Fubini theorem, the Controllability Standard and the Concept of Fractional Calculus to establish results
A study of nonlocal fractional neutral stochastic integrodifferential inclusions of order with impulses
This paper considers a class of nonlocal fractional neutral stochastic
integrodifferential inclusions of order with impulses in a Hilbert
space. We study the existence of the mild solution for the cases when the
multi-valued map has convex and non-convex values. The results are obtained by
combining fixed-point theorems with the fractional order cosine family,
semigroup theory, and stochastic techniques. A new set of sufficient conditions
is developed to demonstrate the approximate controllability of the system.
Finally, an example is given to illustrate the obtained results
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