TOPOLOGICAL STRUCTURE OF SOLUTION SET FOR ψ-HILFER FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACE

Benyoub M., Gülyaz-Öztürk S.

Journal of Mathematical Sciences (United States), 2024 (Scopus) identifier

  • 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.