Akademik Veri Yönetim Sistemi
FILOMAT, cilt.38, sa.25, ss.8755-8772, 2024 (SCI-Expanded)
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.