A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1

2021 ◽  
Author(s):  
C. Dineshkumar ◽  
R. Udhayakumar ◽  
V. Vijayakumar ◽  
Kottakkaran Sooppy Nisar ◽  
Anurag Shukla
Keyword(s):  
Approximate Controllability ◽  
Sobolev Type ◽  
Differential Delay

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 Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

scholarly journals Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Fixed Point ◽  
Linear System ◽  
Fixed Point Theorem ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Complete Controllability ◽  
Approximately Controllable ◽  
Sobolev Type Differential Equations

We discuss the approximate controllability of semilinear fractional Sobolev-type differential system under the assumption that the corresponding linear system is approximately controllable. Using Schauder fixed point theorem, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional Sobolev-type differential equations, are formulated and proved. We show that our result has no analogue for the concept of complete controllability. The results of the paper are generalization and continuation of the recent results on this issue.

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