Optimization of exact controllability for fractional impulsive partial stochastic differential systems via analytic sectorial operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zuomao Yan ◽  
Yong-Hui Zhou
Keyword(s):  
Hilbert Spaces ◽  
Measure Of Noncompactness ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Differential Systems ◽  
New Class ◽  
Sectorial Operators ◽  
State Dependent ◽  
State Dependent Delay

AbstractIn this paper, we consider the optimization problems of exact controllability for a new class of fractional impulsive partial stochastic differential systems with state-dependent delay in Hilbert spaces. By utilizing suitable fixed point approach without imposing severe compactness condition on the operators, the theory of analytic sectorial operators, stochastic analysis, and the Hausdorff measure of noncompactness, some sufficient conditions are derived for achieving the required results. Finally, an example is provided to illustrate the obtained theory.

scholarly journals Approximate controllability of impulsive system involving state-dependent delay and variable delay in control via fundamental solution

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2293-2313
Author(s):  
Syed Abdal ◽  
Surendra Kumar
Keyword(s):  
Fundamental Solution ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Variable Delay ◽  
New Class ◽  
State Dependent ◽  
Semilinear Control Systems ◽  
State Dependent Delay

This article is concerned with the approximate controllability for a new class of impulsive semilinear control systems involving state-dependent delay and variable delay in control in Hilbert spaces. We formulate new sufficient conditions which guarantee the existence of solution to the considered system. We use the theory of fundamental solution, Krasnoselskii?s and Schauder?s fixed point theorems to establish our major results. Finally, two examples are constructed which demonstrate the effectiveness of obtained results.

Approximate controllability of impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces

2018 ◽  
Vol 36 (2) ◽  
pp. 603-622 ◽  
Author(s):  
Yong Zhou ◽  
S Suganya ◽  
M Mallika Arjunan ◽  
B Ahmad
Keyword(s):  
Differential Equation ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Integro Differential Equation ◽  
State Dependent ◽  
State Dependent Delay ◽  
Non Linear ◽  
Approximately Controllable

Abstract In this paper, the problem of approximate controllability for non-linear impulsive fractional integro-differential equation with state-dependent delay in Hilbert spaces is investigated. We study the approximate controllability for non-linear impulsive integro-differential systems under the assumption that the corresponding linear control system is approximately controllable. By utilizing the methods of fractional calculus, semigroup theory, fixed-point theorem coupled with solution operator, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

scholarly journals Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces

2016 ◽  
Vol 24 (1) ◽  
pp. 29-55 ◽  
Author(s):  
S. Kailasavalli ◽  
D. Baleanu ◽  
S. Suganya ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Resolvent Operator ◽  
Exact Controllability ◽  
Differential Systems ◽  
State Dependent ◽  
Banach Contraction ◽  
State Dependent Delay

Abstract In this manuscript, we have a tendency to execute Banach contraction fixed point theorem combined with resolvent operator to analyze the exact controllability results for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. An illustration is additionally offered to exhibit the achieved hypotheses.

Controllability of multi-term time-fractional differential systems with state-dependent delay

2020 ◽  
Vol 26 (2) ◽  
pp. 241-255
Author(s):  
Renu Chaudhary ◽  
Vikram Singh ◽  
D. N. Pandey
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Measure Of Noncompactness ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
State Dependent ◽  
Mönch Fixed Point Theorem ◽  
State Dependent Delay ◽  
Fractional Differential

AbstractIn this paper, controllability results for a class of multi-term time-fractional differential systems with state-dependent delay have been studied. The concept of fractional calculus, measure of noncompactness and Mönch fixed-point theorem has been implemented to obtain a new set of controllability results. Finally, an application is given to illustrate the obtained results.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

Approximate controllability of semilinear impulsive functional differential systems with non-local conditions

2020 ◽  
Vol 37 (4) ◽  
pp. 1070-1088 ◽  
Author(s):  
Sumit Arora ◽  
Soniya Singh ◽  
Jaydev Dabas ◽  
Manil T Mohan
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Local Conditions ◽  
Functional Differential Systems ◽  
Non Local ◽  
Functional Differential

Abstract This paper is concerned with the approximate controllability of semilinear impulsive functional differential systems in Hilbert spaces with non-local conditions. We establish sufficient conditions for approximate controllability of such systems via resolvent operator and Schauder’s fixed point theorem. An application involving the impulse effect associated with delay and non-local conditions is presented to verify our claimed results.

On Fractional Neutral Integro-differential Systems with State-dependent Delay in Banach Spaces

2017 ◽  
Vol 151 (1-4) ◽  
pp. 109-133
Author(s):  
S. Kailasavalli ◽  
S. Suganya ◽  
M. Mallika Arjunan
Keyword(s):  
Banach Spaces ◽  
Differential Systems ◽  
State Dependent ◽  
State Dependent Delay
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