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In the presented paper, authors introduced a new integral transform technique of two parameters “Emad –Israa Transform” with its fundamental properties and solved linear ordinary differential equations with constant coefficients. Numerical problems have taken for visualizing the complete procedure of solution. Results of these problems suggest that the present transform technique of two parameters “Emad- Israa” transform technique provides the outstanding results without dowing tedious computational work.

When attempting to express a differential equation of the first order, it is usual practice to use the equation represented by dy/dx= f(x,y). The above equation contains a function denoted by the notation embodied by f(x,y), defined on a portion of the xy-plane and dependent on two variables, x, and y, which are independent variables. The equation considered to be of the first order is the one that has just the first derivative, which is denoted by the notation dy/dx since there are no higher-order derivatives present in the equation. It is usual practice to make use of the differential equation when attempting to explain the connection that exists between a function and the derivatives of that function. Using this technique to identify functions inside a given domain in physics, chemistry, and many other fields of science is feasible. In order to do so, it is necessary to have previous knowledge about functions and the derivatives of those functions. In this article, the Emad-Sara transformation is presented as a method for identifying the general solution of complex differential equations of the first order that have constant coefficients. This transformation may be used to get the general solution of these equations. This approach, which is both practical and economical, may be used to find solutions to a wide variety of linear operator equations. These equations can range from simple to complex

This article introduces another type of integral transformation in its general format; this general transformation is proposed as a new general integral transformation called the “Emad-Salam-Elaf Transform.” This general integral transformation is elaborated, and its fundamental functions and theorems have been proven. The eligibility of the proposed general integral transform is proven by solving ordinary differential equations of the first and second-order nature.Another type of general integral transform has been studied and proven for some elementary functions, its applicability and ability to evaluate the exact solution have been proven by utilizing the transform to find the solution of first and second order ordinary differential equations.

Differential equations are used to represent different scientific problems are handled efficiently by integral transformations, where integral transforms represent an easy and effective tool for solving many problems in the mentioned fields. This work utilizes the integral transform of the Complex SEE integral transformation to provide an efficient solution method for the difference and differential-difference equations by benefiting from the properties of this complex transform to solve some problems related to difference and differential-difference equations. The 3D, contour and 2D surfaces, as well as the related density plot surfaces of some acquired data, are used to draw the physical aspect of the obtained findings. The proposed approach offers an efficient and rapid solution for addressing the inherent complexity of differential-difference problems with initial conditions. [ABSTRACT FROM AUTHOR]

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In this paper, a new type of integral transform with complex power parameters called the "Mayan transform" has been introduced. The definitions of the integral transform and its inverse are given in the classical case and the corresponding neutrosophic case. The classical analytical properties of the Mayan integral transforms are proven; the application of it to some essential functions and neutrosophic functions is introduced and proven. Also, its application to the neutrosophic derivatives (first, second, and third) then the generalization of the application on the Mayan integral transform on the neutrosophic derivatives are given. The worthiness of the introduced integral transform on the actual application is also proven by applying the integral transform in solving two problems: the response of an Undamped forced mechanical oscillator and the response of an undamped forced electrical oscillator. [ABSTRACT FROM AUTHOR]

The Sadiq-Emad-Emann (SEE) transform, also known as operational calculus, has gained significant importance as a fundamental component of the mathematical knowledge necessary for physicists, engineers, mathematicians, and other scientific professionals. This is because the SEE transform offers accessible and efficient resources for resolving several applications and challenges encountered in diverse engineering and science domains. This study aims to introduce the fundamental principles of SEE transformation and establish the validity of two statements and associated attributes. The objective of this study is to use the aforementioned qualities in order to determine the solution of difference and differential-difference equations, with neutrosophic versions of difference and differential difference equations. In addition, we are able to get very effective and expeditious precise answers. [ABSTRACT FROM AUTHOR]

The medical sector is one of the many scientific domains that may benefit from the use of mathematical models and algorithms to carry out a variety of activities that simplify and improve their job. The models that are utilized in the majority of medical areas are ones that can be anticipated or shaped using mathematical equations. These equations inspire mathematicians to handle them and alter them in order to discover the most accurate and direct form to answer the problems they provide. It's possible that some models of cardiovascular disease have solutions that are more complicated than algebraic models. Therefore, the use of integral transformations in the process of identifying the solutions to the aforementioned equations is quite beneficial. The Emad-Falih integral transformation is used throughout this article to do an analysis of the exact solutions to both of the cardiovascular models being discussed. For the purpose of calculating solutions to ordinary differential equations, the integral transform under study is a technique that is not only practical but also trustworthy and user-friendly. [ABSTRACT FROM AUTHOR]