AbstractIn this paper, we obtain some Hermite-Hadamard type inequalities fors–convex function via fractional integrals with respect to another function which generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. The results presented here provide extensions of those given in earlier works.
In this paper, we are concerned with the ψ-fractional integrals, which is a generalization of the well-known Riemann–Liouville fractional integrals and the Hadamard fractional integrals, and are useful in the study of various fractional integral equations, fractional differential equations, and fractional integrodifferential equations. Our main goal is to present some new properties for ψ-fractional integrals involving a general function ψ by establishing several new equalities for the ψ-fractional integrals. We also give two applications of our new equalities.
Abstract
In the article, we introduce the generalized proportional Hadamard fractional integrals and establish several inequalities for convex functions in the framework of the defined class of fractional integrals. The given results are generalizations of some known results.
In this paper, we introduce some Simpson’s type integral inequalities via the Katugampola fractional integrals for functions whose first derivatives at certain powers are s-convex (in the second sense). The Katugampola fractional integrals are generalizations of the Riemann–Liouville and Hadamard fractional integrals. Hence, our results generalize some results in the literature related to the Riemann–Liouville fractional integrals. Results related to the Hadamard fractional integrals could also be derived from our results.
AbstractIn this paper we establish some trapezoid type inequalities for the Riemann-Liouville fractional integrals of functions of bounded variation and of Hölder continuous functions. Applications for the g-mean of two numbers are provided as well. Some particular cases for Hadamard fractional integrals are also provided.
AbstractThe goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev’s functionals by utilizing a fractional generalized weighted fractional integral involving another function $\mathcal{G}$
G
in the kernel. Also, we present weighted fractional integral inequalities for the weighted and extended Chebyshev’s functionals. One can easily investigate some new inequalities involving all other type weighted fractional integrals associated with Chebyshev’s functionals with certain choices of $\omega (\theta )$
ω
(
θ
)
and $\mathcal{G}(\theta )$
G
(
θ
)
as discussed in the literature. Furthermore, the obtained weighted fractional integral inequalities will cover the inequalities for all other type fractional integrals such as Katugampola fractional integrals, generalized Riemann–Liouville fractional integrals, conformable fractional integrals and Hadamard fractional integrals associated with Chebyshev’s functionals with certain choices of $\omega (\theta )$
ω
(
θ
)
and $\mathcal{G}(\theta )$
G
(
θ
)
.
We present Montgomery identity for Riemann-Liouville fractional integral as well as for fractional integral of a functionfwith respect to another functiong. We further use them to obtain Ostrowski type inequalities involving functions whose first derivatives belong toLpspaces. These inequalities are generally sharp in casep>1and the best possible in casep=1. Application for Hadamard fractional integrals is given.
The author obtains new estimates on generalization
of Hadamard, Ostrowski, and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive real numbers are also given.
We prove new generalization of Hadamard, Ostrowski, and Simpson inequalities in the framework of GA-s-convex functions and Hadamard fractional integral.
On Hermite-Hadamard Type Inequalities for s–Convex Mappings via Fractional Integrals of a Function with Respect to Another Function
