Existence for neutral impulsive differential inclusions with nonlocal conditions

2008 ◽  
Vol 68 (12) ◽  
pp. 3707-3718 ◽  
Author(s):  
Xianlong Fu ◽  
Yueju Cao
Keyword(s):  
Differential Inclusions ◽  
Nonlocal Conditions ◽  
Impulsive Differential Inclusions

scholarly journals Existence of Solutions for Fractional-Order Neutral Differential Inclusions with Impulsive and Nonlocal Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Chao Song ◽  
Tao Zhu ◽  
Jinde Cao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Theoretical Results

This paper investigates the existence of solutions for fractional-order neutral impulsive differential inclusions with nonlocal conditions. Utilizing the fractional calculus and fixed point theorem for multivalued maps, new sufficient conditions are derived for ensuring the existence of solutions. The obtained results improve and generalize some existed results. Finally, an illustrative example is given to show the effectiveness of theoretical results.

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.  

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