Approximate controllability for neutral impulsive differential inclusions with nonlocal conditions

2011 ◽  
Vol 17 (3) ◽  
pp. 359-386 ◽  
Author(s):  
Xianlong Fu
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Impulsive Differential Inclusions

scholarly journals Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Alka Chadha ◽  
Rathinasamy Sakthivel ◽  
Swaroop Nandan Bora
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Nonlinear Differential Inclusions ◽  
Approximately Controllable ◽  
Fractional Differential

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.  

scholarly journals Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhenhai Liu ◽  
Maojun Bin
Keyword(s):  
Control Systems ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Fractional Differential

We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce thePC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.

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