Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces
This paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a <inline-formula&g...
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MDPI AG
2025-03-01
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| author | Faryal Abdullah Al-Adsani Ahmed Gamal Ibrahim |
| author_facet | Faryal Abdullah Al-Adsani Ahmed Gamal Ibrahim |
| author_sort | Faryal Abdullah Al-Adsani |
| collection | DOAJ |
| description | This paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mn>0</mn></msub></semantics></math></inline-formula>-semigroup or a sectorial operator and the nonlinear part is a multi-valued function with convex or nonconvex values. We provide a definition of the mild solutions, and then, by using appropriate fixed-point theorems for multi-valued functions and the properties of both the conformable derivative and the measure of noncompactness, we achieve our findings. We did not assume that the semigroup generated by the linear part is compact, and this makes our work novel and interesting. We give examples of the application of our theoretical results. |
| format | Article |
| id | doaj-art-14b19852dbca4af9a24e090c8c7d2133 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-14b19852dbca4af9a24e090c8c7d21332025-08-20T03:14:14ZengMDPI AGAxioms2075-16802025-03-0114423010.3390/axioms14040230Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach SpacesFaryal Abdullah Al-Adsani0Ahmed Gamal Ibrahim1Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi ArabiaThis paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mn>0</mn></msub></semantics></math></inline-formula>-semigroup or a sectorial operator and the nonlinear part is a multi-valued function with convex or nonconvex values. We provide a definition of the mild solutions, and then, by using appropriate fixed-point theorems for multi-valued functions and the properties of both the conformable derivative and the measure of noncompactness, we achieve our findings. We did not assume that the semigroup generated by the linear part is compact, and this makes our work novel and interesting. We give examples of the application of our theoretical results.https://www.mdpi.com/2075-1680/14/4/230differential inclusionsinfinitesimal generator of a C0-semigroupsectorial operatorconformable fractional derivativeinstantaneous and non-instantaneous impulsesmild solutions |
| spellingShingle | Faryal Abdullah Al-Adsani Ahmed Gamal Ibrahim Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces Axioms differential inclusions infinitesimal generator of a C0-semigroup sectorial operator conformable fractional derivative instantaneous and non-instantaneous impulses mild solutions |
| title | Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces |
| title_full | Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces |
| title_fullStr | Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces |
| title_full_unstemmed | Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces |
| title_short | Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces |
| title_sort | nonlocal conformable differential inclusions generated by semigroups of linear bounded operators or by sectorial operators with impulses in banach spaces |
| topic | differential inclusions infinitesimal generator of a C0-semigroup sectorial operator conformable fractional derivative instantaneous and non-instantaneous impulses mild solutions |
| url | https://www.mdpi.com/2075-1680/14/4/230 |
| work_keys_str_mv | AT faryalabdullahaladsani nonlocalconformabledifferentialinclusionsgeneratedbysemigroupsoflinearboundedoperatorsorbysectorialoperatorswithimpulsesinbanachspaces AT ahmedgamalibrahim nonlocalconformabledifferentialinclusionsgeneratedbysemigroupsoflinearboundedoperatorsorbysectorialoperatorswithimpulsesinbanachspaces |