Our aim in this paper is to introduce new integral transform which we will call it “Battor – AlTememe” transform. This transform is useful for solving many types of differential equations (ordinary and partial) and we will introduce some definitions, concepts and identities. Integral transform is used to solve differential and integral equations. In 2008 [2], the researcher introduced AlTememe transform, which is given by the integral T(f(x))=∫_1^∞▒x^(-p) f(x)dx=F(p), For a function f(x) which is defined on an interval (1, ∞), x^(-p) is the kernel of this transform and p is positive constant such that the above integral is converge.
As an important type of integral equation, Volterra integral equations snatch the focus of many scientists and mathematicians to provide approximate or exact solutions to such equations. The integral transform capability of providing an algebraic solution to the integral equations led the mathematical community to lean heavily on them to solve those kinds of equations, including the Volterra integrodifferential equations of the second kind. This paper uses the complex SEE integral transform to find the exact solution to the second kind linear Volterra integrodifferential equation. The capability and efficiency of complex SEE integral transform in providing an exact solution with the minimum number of computations possible are demonstrated via practical applications.
In this article , we developed the general polynomial transform into a new transform ( Ahmad - Emad - Murat transform ) , which was expanded by writing a general formula of the Kernel function K ( x , t ) . Besides , we presented the essential characteristics and theorems of AEM transform and made new results. In addition , the efficiency of the proposed transform was verified by applying it to a set of important examples , the most important one is “ Cauchy Euler problems ” . The main advantage of the proposed transform is getting a more generalized transform and making it easier to handle in solving differential equations with variable coefficients , reducing effort and time in the calculations . Hence , the polynomial integral transform and general polynomial transform that have been introduced during the last years are special transforms of the AEM transform .
The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations
In this paper, the suggested transform namely (Sadiq- Emad- Jinan) integral transform and denoted by "SEJI" integral transform is applied to solve a linear second-order delay differential equation with the initial-value problem for the equation. Firstly, we introduce the form of this equation and provide examples of its use in a wide variety of scientific disciplines. Then the proposed transform is defined and describe its essential features as well as the value of the SEJI integral transform for derivatives. After that, proved a theorem for getting the precise answer by using "SEJI integral transform". The theoretical results were illustrating by a concrete example as presented above. As a result, an appropriate conclusion was introduced for this work.
In this paper, a modification on Poisson partial differential equation has been performed, the applied modification has increased the domain and range of Poisson equation. The novel integral transformation "Al-Zughair" has been used to solve the improved Poisson and heat partial differential equations, as a new solving method for some partial differential equations.
Abstract Due to the worldwide expansion of the internet, the consumption and transmission of multimedia materials have risen significantly. This growth in demand necessitated a corresponding increase in data security measures. This work investigates encryption technology and proposes a novel color picture encryption and decryption approach based on the “SEE transform” developed by Sadiq, Emad, and Eman. We used the SEE transform to encrypt the original image, and the corresponding inverse SEE transform for decryption. The SEE transform has been performed to enhance the security of the encryption method. After using the SEE transform, we show that the suggested method considerably improves security measures and immunity to attacks, as demonstrated by comprehensive experiments and statistical analysis.
Abstract In the modern time, Bessel’s functions appear in solving many applications of engineering and natural science together with many equations such as Schrodinger equation, Laplace equation, heat equation, wave equation and Helmholtz equation in cylindrical or spherical coordinated, in this work, we introduce complex SEE integral transform of Bessel’s functions with some important applications of complex SEE transform of Bessel’s functions for evaluating the integral, which contain Bessel’s functions, are given.
'/%3e%3cpath fill='%23fff' d='m8.751-17.959 10.11 11.373L3.997-9.844l13.94-6.1-7.692 13.129z'/%3e%3c/svg%3e)
 scale(2.18978)'%3e%3cpath d='M246.026 120.178c-.558-.295-1.186-.768-1.395-1.054-.314-.438-.132-.456 1.163-.104 2.318.629 3.814.383 5.298-.873l1.308-1.103 1.54.784c.848.428 1.748.725 2.008.656.667-.176 2.05-1.95 2.005-2.564-.054-.759.587-.568.896.264.615 1.631-.281 3.502-1.865 3.918-.773.201-1.488.127-2.659-.281-1.438-.502-1.684-.494-2.405.058-1.618 1.239-3.869 1.355-5.894.299zm5.734-5.242c-.563-.717-1.239-3.424-1.021-4.088.192-.576.391-.691.914-.527.918.287 1.13.92.993 3.064-.107 1.747-.366 2.206-.886 1.551zm-67.516-1.946c-.185 1.311 2.325 4.568 3.458 5.158-.77.345-1.728.188-2.434.576-3.948 3.948-18.367 18.006-21 21.366 7.799.154 16.448-.106 23.761-.44-.007-5.299 5.018-5.572 8.381-7.502 1.73 2.725 6.075 2.516 6.618 6.617 0 4.91.009 12.307.009 17.646h-66.625c-1.172 5.176-5.844 9.125-12.354 7.5 2.014-2.104 5.405-2.827 6.619-5.734 1.024-6.365-2.046-10.296-4.031-13.906 3.284-1.195 3.782-1.494 7.121-3.737-2.344 7.12 6.091 6.338 12.353 6.175.211-2.417.089-5.271-1.766-5.624 2.396-.87 2.794-1.168 6.619-4.412v9.593c14.886 0 30.942-.111 46.139-.111 0-3.002.795-7.824-1.581-7.824-2.269 0-.107 6.173-1.87 6.173h-35.63c0-1.328-.034-4.104-.034-6.104 1.51-1.51 1.331-1.379 11.648-11.697 1.028-1.031 8.266-7.568 14.599-13.713zm89.06-.254c2.487 1.339 4.457 3.191 7.502 3.972-.354 1.261-1.476 1.759-1.77 3.087v26.91c3.402.75 4.118-1.178 5.737-2.205.442 4.307 3.186 8.529 3.088 11.91h-14.559c.002-14.555.002-29.114.002-43.674zm-19.412 14.412s5.296-4.471 5.296-4.643v23.484l3.814-.006c0-8.947-.118-18.022-.118-26.338 1.548-1.549 4.58-3.791 5.338-5.358v42.06c-10.746 0-30.793.012-33.443.012-.493-8.729-.577-17.771 9.6-15.826v-3.563c-.311-.609-.868.147-.998-.645 1.615-1.617 2.163-2.029 6.538-5.852 0 4.612.08 15.5.08 15.5 1.07 0 3.153.004 3.857.004.001.002.036-18.227.036-18.829zm-12.553 18.603c.716 1.075 3.154 1.056 3.04-.755-.411-1.493-3.616-.924-3.04.755z'/%3e%3ccircle cx='144.527' cy='161.369' r='2.042'/%3e%3cpath d='M207.549 112.779c2.488 1.339 4.457 3.191 7.502 3.971-.353 1.26-1.476 1.76-1.768 3.087v26.911c3.401.749 4.117-1.18 5.736-2.206.441 4.308 3.185 8.528 3.088 11.91h-14.56c.002-14.556.002-29.114.002-43.673z'/%3e%3c/g%3e%3c/svg%3e)
