In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this 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. 

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.

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.

Resumen

                       Este trabajo de investigación ofrece uno de los temas relevantes en la lengua, el cual es estudiar las dimensiones sintácticas, semánticas y pragmáticas de las preposiciones, en general, y de las dos preposiciones "Para" y  "Por" en concreto, en una unidad linguística más amplia que la llamada "Oración". En la parte  referida al  estudio de las dos preposiciones mencionadas,  estudiamos sus distntos usos funcionales, usos que se acercan, unas veces,  entre sí  y  se alejan en otras. 

Abstract    

Le but de la présente étude est de mettre en lumière la fragilité des personnages dans le roman de "Mme Bovary". En fait, la fragilité n'est pas uniquement propre aux héros de Flaubert. Nous pouvons attribuer cette caractéristique à la plupart des protagonistes du XIX^e siècle. Nous pouvons dire qu'aucun auteur n'excelle autant que Flaubert à incarner cette fragilité.

                Flaubert présente un personnage frustré de toute force et de toute volonté comme le personnage d'Emme Bovary.

                Ce personnage n'a pas de confiance en soi, E