Journal
INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL
Volume 10, Issue 5, Pages 1613-1625Publisher
SPRINGERNATURE
DOI: 10.1007/s40435-021-00887-0
Keywords
Fractional dynamic inclusions; Controllability; Nonlocal conditions; Non-instantaneous impulses; Fractional derivative; Nondense domain; Set-valued operator; Integral solution; Fixed point
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This article investigates the controllability of a class of nondensely defined fractional dynamic delay inclusions containing Hilfer fractional derivative, nonlocal conditions, and non-instantaneous impulses in abstract spaces without the compactness assumption. The existence of an integral solution and the controllability of the given problem are established using a condensing fixed point theorem of multivalued maps. An example is provided to clarify the obtained theoretical outcomes.
The controllability of a class of nondensely defined fractional dynamic delay inclusions containing Hilfer fractional derivative, nonlocal conditions, and non-instantaneous impulses in abstract spaces is investigated without compactness assumption. The existence of an integral solution and the controllability for the given problem are established relying on a condensing fixed point theorem of multivalued maps. In support, an example is given to clarify the obtained theoretical outcomes.
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