In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions. 

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

Market share is a major indication of business success. Understanding the impact of numerous economic factors on market share is critical to a company’s success. In this study, we examine the market shares of two manufacturers in a duopoly economy and present an optimal pricing approach for increasing a company’s market share. We create two numerical models based on ordinary differential equations to investigate market success. The first model takes into account quantity demand and investment in R&D, whereas the second model investigates a more realistic relationship between quantity demand and pricing.

Background: Oral Lichen Planus is a chronic inflammatory mucosal disease, presenting in various clinical forms .Both antigen-specific and non-specific mechanisms involved in the pathogenesis of OLP. Apoptosis or programmed-cell death is a physiological process essential for the normal development and maintenance of homeostasis in many organisms. Fas is a cell-surface glycoprotein, 40-kDa, that belongs to the nerve growth factor / tumor necrosis factor (TNF) receptor family. Fas is expressed in several tissues including blood, where its expression is upregulated on activated T and B lymphocytes and natural killer cells. Fas ligand is a type II transmembrane protein that belongs to the tumor necrosis factor family. The proto-oncogene c-Myc is

ABSTRACT Background: Neuropilin 1(NRP1) is considered a novel non - tyrosine kinase co- receptor for the vascular endothelial growth factors (VEGF). First discovered on migrating neurons. NRP1is suggested to be up-regulated in cells of different types of cancer and implicated with advanced disease. The aim of this study was to investigate the variation in expression of NRP1 in oral, laryngeal and skin squamous cell carcinoma. Materials and methods: Tissue sections from 120 formalin fixed- paraffin embedded blocks histopathologically diagnosed as oral, laryngeal and skin SCC (40 blocks for each),immunohistohemically stained in immunoperoxidase method with monoclonal antibodies to NRP1, the localization of expression was examined and the res