No abstract

In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ. The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Ψ and the proportionality index ς. Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.

Abstract:In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.

We established a new Hermit-Hadamard type inequality for GA-convex functions. As applications, we obtain two new Gautschi type inequalities for gamma function.

Boron nitride nanotubes (BNNTs) have been increasingly investigated for use in a wide range of applications due to their unique physicochemical properties including high hydrophobicity, heat and electrical insulation, resistance to oxidation, and hydrogen storage capacity. They are also valued for their possible medical and biomedical applications including drug delivery, use in biomaterials, and neutron capture therapy. Chemical graph theory provides different tools to investigate different properties of nanotubes. Tools like topological invariants are useful to associate an appropriate number with a networks through which we can guess different hidden properties of under consideration network. There are more then 150 topological indices present in history, but no one gives use perfect result in predicting properties of networks. So there is always a room to introduce some new invariants that help us to gain better results. In this paper, we will introduce some new topological indices and polynomials, namely, Maxmin indices and Maxmin polynomials and, calculate results for three different boron nanotubes, boron triangular nanotube BT[p, q], boron‐α nanotube BT(X)[p, q] and boron‐α nanotube BT(Y)[p, q].