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.
Highlights
In recent years, fractional calculus has been applied in many real processes, and notable contributions have been made to both theory and applications of fractional differential equations
Motivated by the previous works, in this paper, we investigate the approximate controllability of the following integro-differential inclusions involving nonlocal conditions in a separable Banach space (E, · ) in the following form: t s
Very few works are available in the literature, which deal with solvability and approximate controllability of nonlocal differential inclusion involving fractional derivative utilizing measure of noncompactness
Summary
Fractional calculus has been applied in many real processes, and notable contributions have been made to both theory and applications of fractional differential equations. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is only in its initial stage of development. This is essential since differential models involving the fractional derivative give a brilliant tool for depiction of memory and genetic properties, and have recently been demonstrated as significant tools in the modeling of many physical phenomena. We attempt to consider the approximate controllability of fractional nonlocal differential inclusion using measure of noncompactness instead of assuming compactness of sectorial operator. Motivated by the previous works, in this paper, we investigate the approximate controllability of the following integro-differential inclusions involving nonlocal conditions in a separable Banach space (E, · ) in the following form:.
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