On a fractional differential inclusion involving a generalized Caputo type derivative with certain fractional integral boundary conditions
Keywords:differential inclusion, fractional derivative, measurable selection. 2010 MSC: 34A60, 26A33, 34B15
We study a class of fractional differential inclusions defined by Caputo-Katugampola fractional derivative
involving a nonconvex set-valued map in the presence of certain fractional integral boundary conditions.
Using a technique developed by Filippov we establish an existence result for the problem considered under
the hypothesis that the set-valued map is Lipschitz in the state variable. Also, based on a result concerning
the arcwise connectedness of the fixed point set of a class of set-valued contractions, we prove the arcwise
connectedness of the solution set of the problem considered. The paper is the first in literature which contains
such kind of results in the framework of the problem studied.
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