Higher-order boundary value problems for Carathéodory differential inclusions

Aitalioubrahim, Myelkebir; Sajid, Said

doi:10.18514/mmn.2008.180

Cited by 7 publications

(2 citation statements)

References 3 publications

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“…We present some concepts regarding the multifunctions (set-valued maps) [41]. For this aim, consider the Banach space (C, • ) and S : C → P(C) as a multifunction that:…”

Section: Multifunction Theorymentioning

confidence: 99%

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A generalized neutral-type inclusion problem in the frame of the generalized Caputo fractional derivatives

et al. 2021

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In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of $( \vartheta (t)-\vartheta (s)) $ ( ϑ ( t ) − ϑ ( s ) ) along with differential operator $\frac{1}{\vartheta '(t)}\,\frac{\mathrm{d}}{\mathrm{d}t}$ 1 ϑ ′ ( t ) d d t . We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results.

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“…We present some concepts regarding the multifunctions (set-valued maps) [41]. For this aim, consider the Banach space (C, • ) and S : C → P(C) as a multifunction that:…”

Section: Multifunction Theorymentioning

confidence: 99%

“…For other notions such as the complete continuity or upper semicontinuity (u.s.c. ), see [41]. Furthermore, the set of selections of H is given by…”

Section: Multifunction Theorymentioning

confidence: 99%