Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions
Articles
Alka Chadha
Indian Institute of Technology Guwahati
Rathinasamy Sakthivel
Bharathiar University
Swaroop Nandan Nandan Bora
Indian Institute of Technology Guwahati
Published 2019-06-27
https://doi.org/10.15388/NA.2019.4.2
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Keywords

approximate controllability
measure of noncompactness
multivalued map
fractional differential inclusions
resolvent operator

How to Cite

Chadha, A., Sakthivel, R. and Bora, S.N.N. (2019) “Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions”, Nonlinear Analysis: Modelling and Control, 24(4), pp. 503–522. doi:10.15388/NA.2019.4.2.

Abstract

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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