Convexity performs the appropriate role in theoretical study of inequalities according to nature and behaviour. There is a strong relation between symmetry convexity. In this article, we consider new parameterized quantum fractional integral identity. Following that, our main results are established, which consist some Ostrowski midpoint type pertaining n-polynomial convex functions. From resul...

The second part of Hilbert’s sixteenth problem concerned with the existence and number of the limit cycles for planer polynomial differential equations of degree n. In this article after a brief review on previous studies of a particular class of Hilbert’s sixteenth problem, we will discuss the existence and the stability of limit cycles of this class in the form of fractional differential equa...

One-dimensional (1D) model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green’s function (hole propagator) at any rational interaction coupling constant λ = p/q a...

This contribution presents an overview of sensitivity analysis of simulation models, including the estimation of gradients. It covers classic designs and their corresponding (meta)models; namely, resolution-III designs including fractional-factorial twolevel designs for …rst-order polynomial metamodels, resolution-IV and resolution-V designs for metamodels augmented with twofactor interactions,...

A lot of problems involve unknown data relations, which can define a derivative based model of dependent variables generalization. Standard softcomputing methods (as artificial neural networks or fuzzy rules) apply usual absolute interval values of input variables. The new proposed differential polynomial neural network makes use of relative data, which can better describe the character regardi...

We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three–manifolds in the case of quadratic nonlinearities. We also discuss the optimali...

In a general fractional factorial design the n levels of each factor are coded by the n-th roots of the unity. This device allows a full generalization to mixed designs of the theory of polynomial indicator function already introduced for binary designs by Fontana and the Authors (2000). Properties of orthogonal arrays and regular fractions are discussed.

This paper is concerned with a class of ten time-fractional polynomial evolution equations. The one-parameter Lie point symmetries these equations are found and the symmetry reductions provided. These reduced transformed into nonlinear ordinary differential equations, which challenging to solve by conventional methods. We search for power series solutions demonstrate convergence properties such...