Generalized AB-Fractional Operator Inclusions of Hermite-Hadamard's Type via Fractional Integration

Bin-Mohsin B., Awan M. U., Javed M. Z., Khan A. G., Budak H., Mihai M. V., ...Daha Fazla

SYMMETRY-BASEL, cilt.15, sa.5, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 5
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/sym15051012
  • Dergi Adı: SYMMETRY-BASEL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function E-mu,alpha,l(gamma,delta, k,c) (tau; p) as a kernel in the interval domain. Additionally, a new form of Atangana-Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in E-mu,alpha,l(gamma,delta, k,c)(tau; p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite-Hadamard, Pachapatte, and Hermite-Hadamard-Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases.