On generalized ψ-conformable calculus: Properties and inequalities


Azzouz N., Benaissa B., Budak H.

FILOMAT, vol.38, no.25, pp.8755-8772, 2024 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 38 Issue: 25
  • Publication Date: 2024
  • Doi Number: 10.2298/fil2425755a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.8755-8772
  • Kocaeli University Affiliated: No

Abstract

In this paper, we first introduce a new fractional derivatives and integrals called generalized psi-conformable derivative and generalized psi-conformable integral operators, respectively. We also show that these operators generalize various well-known fractional integral operators. Then, we present several properties of these operators including semi-group property. Moreover, we apply these operators to obtain a new Hermite-Hadamard-type inequality for convex functions. Furthermore, we obtain corresponding midpoint and trapezoid type inequalities for functions whose derivatives in absolute value are convex.