On nabla conformable fractional Hardy-type inequalities on arbitrary time scales

The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.

Steffensen-Type Inequalities with Weighted Function via (γ, a)-Nabla-Conformable Integral on Time Scales

The primary goal of this our research is to prove several new ∇-conformable dynamic Steffensen inequalities that were demonstrated in recent works. Our results generalize and extend existing results in the literature. Many special cases of the proposed results are obtained and analyzed such as new conformable fractional sum inequalities and new classical conformable fractional integral inequalities.

New integral inequalities for geometrically convex functions via conformable fractional integral operators

We establish several basic inequalities versions of the Hermite-Hadamard type inequalities for GA− and GG−convexity for conformable fractional integrals. Several special cases are also discussed, which can be deduced from our main result.

Approximation of functions by Complex conformable derivative bases in Frechet spaces

In the present paper the representation, in different domains, of analytic functions by complex conformable fractional derivative bases (CCFDB) and complex conformable fractional integral bases (CCFIB) in Frechet space are investigated . Theorems are proved to show that such representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin and for all entire functions. Also, some results concerning the growth order and type of CCFDB and CCFIB are determined. Moreover the T-property of CCFDB and CCFIB are dis- cussed. The obtained results recover some known results when alpha = 1. Finally, some applications to the CCFDB and CCFIB of Bernoulli, Euler, Bessel and Chebyshev polynomials have been studied.

On the weighted fractional Pólya–Szegö and Chebyshev-types integral inequalities concerning another function

The primary objective of this present paper is to establish certain new weighted fractional Pólya–Szegö and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function Ψ in the kernel. The inequalities presented in this paper cover some new inequalities involving all other type weighted fractional integrals by applying certain conditions on $\omega (\theta )$ ω ( θ ) and $\Psi (\theta )$ Ψ ( θ ) . Also, the Pólya–Szegö and Chebyshev type integral inequalities for all other type fractional integrals, such as the Katugampola fractional integrals, generalized Riemann–Liouville fractional integral, conformable fractional integral, and Hadamard fractional integral, are the special cases of our main results with certain choices of $\omega (\theta )$ ω ( θ ) and $\Psi (\theta )$ Ψ ( θ ) . Additionally, examples of constructing bounded functions are also presented in the paper.

New Modified Conformable Fractional Integral Inequalities of Hermite–Hadamard Type with Applications

In this study, a few inequalities of Hermite–Hadamard type are constructed via the conformable fractional operators so that the normal version is recovered in its limit for the conformable fractional parameter. Finally, we present some examples to demonstrate the usefulness of conformable fractional inequalities in the context of special means of the positive numbers.