New discussion about the approximate controllability of fractional stochastic differential inclusions with order 1 <  r  < 2

2021 ◽  
Author(s):  
C. Dineshkumar ◽  
Kottakkaran Sooppy Nisar ◽  
R. Udhayakumar ◽  
V. Vijayakumar
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Stochastic Differential Inclusions

Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type

2021 ◽  
Vol 151 ◽  
pp. 111264
Author(s):  
K. Kavitha ◽  
V. Vijayakumar ◽  
Anurag Shukla ◽  
Kottakkaran Sooppy Nisar ◽  
R. Udhayakumar
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Clarke Subdifferential ◽  
Sobolev Type

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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