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Study of (k,Θ)-Hilfer fractional differential and inclusion systems on the glucose graph
- Source :
- Heliyon, Vol 10, Iss 10, Pp e31285- (2024)
- Publication Year :
- 2024
- Publisher :
- Elsevier, 2024.
-
Abstract
- This article combines (k,Θ)-Hilfer fractional calculus with glucose molecular graph, defines fractional differential and inclusion systems on each edge of a glucose molecular graph by the assumption that 0 or 1 marks the vertices, and studies the single-valued and multi-valued (k,Θ)-Hilfer type fractional boundary value problems on the glucose molecular graph. On the one hand, the existence and uniqueness of solutions in the single-valued case are proved by using several fixed point theorems. On the other hand, in the multi-valued case, we consider that the right side of the inclusion has convex valued and non-convex value. By applying Leray-Schauder nonlinear alternative method of multi-valued maps as well as Covitz-Nadler fixed point theorem of multi-valued contractions, two existence results are obtained respectively. On this basis, we also get the topological structure of the solution set, which is a pioneering work for (k,Θ)-Hilfer fractional differential inclusion on the glucose graph. Finally, several examples are provided to verify the reliability of our proposed results.
Details
- Language :
- English
- ISSN :
- 24058440
- Volume :
- 10
- Issue :
- 10
- Database :
- Directory of Open Access Journals
- Journal :
- Heliyon
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.06c7704b24fc4ce99f7a089310a51927
- Document Type :
- article
- Full Text :
- https://doi.org/10.1016/j.heliyon.2024.e31285