Abstract
A coupled system of Hilfer fractional differential inclusions with nonlocal integral boundary conditions is considered. An existence result is established when the set-valued maps have non-convex values. We treat the case when the set-valued maps are Lipschitz in the state variables and we avoid the applications of fixed point theorems as usual. An illustration of the results is given by a suitable example.
Highlights
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The approach we present here avoids the applications of fixed point theorems and takes into account the case when the values of F1 and F2 are not convex; but these set-valued maps are assumed to be Lipschitz in the second and third variable
Even if the technique used here may be seen at other classes of coupled systems of fractional differential inclusions [13–15], to the best of our knowledge, the present paper is the first in literature which contains an existence result of Filippov type for coupled systems of Hilfer fractional differential inclusions
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Where F1 (., ., .) : [ a, b] × R2 → P (R), F2 (., ., .) : [ a, b] × R2 → P (R) are given set-valued α,β maps, D H is the Hilfer fractional derivative of order α and type β, I φ is the Riemann–. The approach we present here avoids the applications of fixed point theorems and takes into account the case when the values of F1 and F2 are not convex; but these set-valued maps are assumed to be Lipschitz in the second and third variable. In this case, we establish an existence result for problems (1) and (2). Even if the technique used here may be seen at other classes of coupled systems of fractional differential inclusions [13–15], to the best of our knowledge, the present paper is the first in literature which contains an existence result of Filippov type for coupled systems of Hilfer fractional differential inclusions
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