TOPOLOGICAL STRUCTURE OF SOLUTION SET FOR ψ-HILFER FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACE
Journal of Mathematical Sciences (United States), 2024 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2024
- Doi Numarası: 10.1007/s10958-024-07399-0
- Dergi Adı: Journal of Mathematical Sciences (United States)
- Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, MathSciNet, zbMATH
- Anahtar Kelimeler: Condensing map, Measure of noncompactness, Rδ-set, ψ-Hilfer fractional derivative
- Sivas Cumhuriyet Üniversitesi Adresli: Evet
Özet
In this paper, we investigate the topological structure of the solution set for the initial value problem associated with ψ-Hilfer fractional differential equations in Banach space. We show that the solution set of the fractional Cauchy problem is nonempty, compact, and an Rδ-set. This result allows to apply a fixed result for condensing maps in the weighted space of continuous functions. Finally, an example to illustrate the applications of the main result is also given.