Innovative Journal of Mathematics (IJM)

Integral Inequalities for Generalized Approximately h-convex Functions on Fractal Sets via Generalized Local Fractional Integrals

2022-07-01T16:57:56+00:00

The present paper study the notion of generalized approximately h-convex function and define a novel generalized fractional integral operator on fractal sets. We derive local fractional integral inequalities involving newly defined generalized local fractional
integral operator for generalized approximately h-convex function. Special cases of the results are also established.

Nonlinear Models by Parameters and their Transformation

2022-07-03T20:45:02+00:00

The development of nonlinear models is presented as a need to carry out various researches which cannot be achieved through linear models. Some of the concepts that will be elaborated are the meaning of nonlinear regression, the general form of nonlinear models, the separation of nonlinear models and some applications of nonlinear models through SPSS. We will also explain the way of realizing the transformation of nonlinear models in simpler and more convenient forms of work.

Product and Quotient of Inverse Paralogistic Distribution Generated Based on Farlie-Gumbel-Morgenstern (FGM) Copula

2022-07-03T20:43:33+00:00

In this article, Inverse Paralogistic distribution based on Farlie-Gumbel-Morgenstern (FGM) copula is introduced. Derivations of exact distribution V = XY ,W = X/Y , and Z = X/(X + Y ) are obtained in closed form. Corresponding moment properties of these distributions are also derived. The expressions turn out to involve known special functions.

Norm Equalities and Inequalities for Operator Matrices

2022-05-31T10:30:46+00:00

The aim of this thesis is to study some Norm equalities and Inequalities for operator Matrices and some of their properties. Also, we present the aim of this thesis to present some famous norm inequalities for Hilbert space operators which have been studied in literature and some new results.

Novel Results for the Stability of h-Discrete Fractional Neural Networks with Nonsingular and Nonlocal Kernels

2022-07-01T16:53:26+00:00

We investigate at a novel type of nonlinear discrete-time fractional neural networks using the h-discrete nabla ABC fractional operator. To derive appropriate criteria for the existence and uniqueness of solutions to the issues at hand, we apply basic fixed-point theory techniques. Furthermore, The Ulam-Hyers stability of the considered model, as well as significant findings, are shown. Moreover, to highlight the validity of the presented conclusions, two and three-dimensional examples are explored.

Analysis of Heat Transfer of Power-Law Fluid Along a Vertical Stretching Cylinder

2022-06-20T19:43:19+00:00

The aim of this paper is to study the heat transfer enhancement of power-law fluid over a vertical stretching cylinder. The model is governed by partial differential equations (PDEs) which is then converted into a coupled system of non-linear ordinary differential equations (ODEs). Here both velocity and temperature profiles have been constructed for different physical parameters such as, Reynold number, Prandtl number, Eckert number, unsteadiness, mixed convective and magnetic-parameters. The obtained results have been compared with the existing literature that reveals the accuracy of the proposed scheme. Moreover, it has been noticed during the study that the power-law energy is getting enhanced corresponding to these parameters, which can be viewed in graphical simulations. In addition, the numerical computations of local-skin friction coefficient and Nusselt number are tabulated.

A Regularity in Ramanujan Summation Function Results for the Triangular Number Series

2022-07-01T16:54:40+00:00

The Triangular Number Series, defined as 1 + 2 + 3 + 4 + ..., when subjected to Ramanujan Summation, gives the known and somewhat controversial result of -1/12. The Ramanujan Summation Function is defined in such a way as to accept any such series and produce corresponding values for them, thus allowing for the aforementioned result to be obtained as well. In this paper, the Triangular Number Group Series Function is defined as a function that generates members of a sum, whereas the values of those members depend on a parameter g, representing the number of elements from the Triangular Number Series in each member of the new sum. This paper shows that the results of the Ramanujan Summation Function upon any such Triangular Number Group Series follow a regularity that is also dependent on the parameter g. Once such a regularity is obtained, the scope of g is extended to real and complex numbers as well.

Average No Regret Sentinel

2022-07-01T16:52:48+00:00

In this paper, we consider a wave equation with pollution term that includes a fractional derivative of Riemann- Liouville with missing Newman boundary condition and the operator depending on unknown parameter. First we try to avoid the unknown parameter and to isolate the missing function the results are established by introduce the notion of average no regret sentinel. Second is applied the classical approach of sentinel to identify the pollution.