On generalized ψ-conformable calculus: Properties and inequalities
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.