GENERAL<i> ((k,</i><i> p</i> ) , ψ)-HILFER FRACTIONAL INTEGRALS

Benaissa B., Budak H.

MISKOLC MATHEMATICAL NOTES, vol.25, no.2, pp.617-627, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.18514/mmn.2024.4594
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.617-627
  • Kocaeli University Affiliated: No

Abstract

The main motivation of this study is to establish a general version of the RiemannLiouville fractional integrals with two exponential parameters k and p called ((k, p),psi)-Hilfer fractional integrals which is determined over the k-gamma function. We first prove that these operators are well-defined, continuous and have semi-group property. Then, particularly, we present the harmonic, geometric and arithmetic (k, p), psi-Hilfer fractional integrals. Moreover, some special cases relating to general ((k, p),psi)-Riemann-Liouville fraction integrals are given.