On the weighted fractional integral inequalities for Chebyshev functionals

The 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 ) .

SIMPSON’S TYPE INEQUALITIES VIA THE KATUGAMPOLA FRACTIONAL INTEGRALS FOR s-CONVEX FUNCTIONS

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.

New generalized Pólya–Szegö and Čebyšev type inequalities with general kernel and measure

It is always attractive and motivating to acquire the generalizations of known results. In this article, we introduce a new class $\mathfrak{C(h)}$ C ( h ) of functions which can be represented in a form of integral transforms involving general kernel with σ-finite measure. We obtain some new Pólya–Szegö and Čebyšev type inequalities as generalizations to the previously proved ones for different fractional integrals including fractional integral of a function with respect to another function capturing Riemann–Liouville integrals, Hadamard fractional integrals, Katugampola fractional integral operators, and conformable fractional integrals. This new idea shall motivate the researchers to prove the results over a measure space with general kernels instead of special kernels.

Trapezoid type inequalities for generalized Riemann-Liouville fractional integrals of functions with bounded variation

In 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.

Hardy’s inequalities and integral operators on Herz-Morrey spaces

We obtain some estimates for the operator norms of the dilation operators on Herz-Morrey spaces. These results give us the Hardy’s inequalities and the mapping properties of the integral operators on Herz-Morrey spaces. As applications of this general result, we have the boundedness of the Hadamard fractional integrals on Herz-Morrey spaces. We also obtain the Hilbert inequality on Herz-Morrey spaces.

Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets

In this study, we establish new integral inequalities of the Hermite–Hadamard type for s-convexity via the Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann–Liouville into a single form. We show that the new integral inequalities of Hermite–Hadamard type can be obtained via the Riemann–Liouville fractional integral. Finally, we give some applications to special means.

Certain inequalities via generalized proportional Hadamard fractional integral operators

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.

Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications

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.

New Hermite-Hadamard type inequalities for convex mappings utilizing generalized fractional integrals

In this work, we first establish new Hermite-Hadamard inequalities for convex function utilizing fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover, we obtain some generalized midpoint and trapezoid type inequalities for these kinds of fractional integrals. The inequalities given in this paper provide generalizations of several results obtained in earlier works.