Towards new general double integral transform and its applications to differential equations

2021 ◽  
Author(s):  
Meryem Meddahi ◽  
Hossein Jafari ◽  
Xiao‐Jun Yang
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
Double Integral

scholarly journals Laplace–Elzaki Transform and its Properties with Applications to Integral and Partial Differential Equations: تحويل لابلاس-الزاكي وخواصه مع تطبيقاته على المعادلات التكاملية والتفاضلية الجزئية

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Safaa Adnan Shaikh Al-Sook, Mohammad Mahmud Amer
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Transform ◽  
Convolution Theorem ◽  
Double Integral ◽  
Partial Differential ◽  
Function Of Two Variables

  Laplace-Elzaki transform (LET) as a double integral transform of a function  of two variables was presented to solve some integral and partial differential equations. Main properties and theorems were proved. The convolution of two function  and  and the convolution theorem were discussed. The integral and partial differential equations were turned to algebraic ones by using (LET) and its properties. The results showed that the Laplace-Elzaki transform was more efficient and useful to handle such these kinds of equations.    

scholarly journals Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform)

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Shams A. Ahmed ◽  
Tarig M. Elzaki ◽  
Abdelgabar Adam Hassan
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
Convolution Theorem ◽  
Double Integral ◽  
Sumudu Transform ◽  
Integral Differential Equations

The primary purpose of this research is to demonstrate an efficient replacement double transform named the Laplace–Sumudu transform (DLST) to unravel integral differential equations. The theorems handling fashionable properties of the Laplace–Sumudu transform are proved; the convolution theorem with an evidence is mentioned; then, via the usage of these outcomes, the solution of integral differential equations is built.

scholarly journals Applications of New Double Integral Transform (Laplace–Sumudu Transform) in Mathematical Physics

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shams A. Ahmed
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Transform ◽  
Mathematical Physics ◽  
High Accuracy ◽  
Double Integral ◽  
Partial Differential ◽  
Fundamental Properties ◽  
Sumudu Transform ◽  
Basic Functions

The primary purpose of this research is to demonstrate an efficient replacement of double transform called the double Laplace–Sumudu transform (DLST) and prove some related theorems of the new double transform. Also, we will discuss the fundamental properties of the double Laplace–Sumudu transform of some basic functions. Then, by utilizing those outcomes, we will apply it to the partial differential equations to show its simplicity, efficiency, and high accuracy.

scholarly journals Some Schemata for Applications of the Integral Transforms of Mathematical Physics

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 254 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
First Integral ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Basic Properties ◽  
Survey Article ◽  
Laplace Integral ◽  
Generating Operators

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

scholarly journals A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1216 ◽  
Author(s):  
Elina Shishkina ◽  
Sergey Sitnik
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Integral Transform ◽  
Bessel Operator ◽  
Explicit Solutions ◽  
Solutions To Equations ◽  
Fractional Powers ◽  
Derivatives Of ◽  
Fractional Equation

In this article we propose and study a method to solve ordinary differential equations with left-sided fractional Bessel derivatives on semi-axes of Gerasimov–Caputo type. We derive explicit solutions to equations with fractional powers of the Bessel operator using the Meijer integral transform.

scholarly journals Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application

2021 ◽  
Vol 5 (3) ◽  
pp. 130
Author(s):  
Ahmed Ibrahim El-Mesady ◽  
Yaser Salah Hamed ◽  
Abdullah M. Alsharif
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Integral Transform ◽  
Inverse Operator ◽  
Integral Transforms ◽  
Delta Function ◽  
Medical Application ◽  
Heaviside Function ◽  
Algebraic Equations ◽  
General Integral

Integral transformations are essential for solving complex problems in business, engineering, natural sciences, computers, optical science, and modern mathematics. In this paper, we apply a general integral transform, called the Jafari transform, for solving a system of ordinary differential equations. After applying the Jafari transform, ordinary differential equations are converted to a simple system of algebraic equations that can be solved easily. Then, by using the inverse operator of the Jafari transform, we can solve the main system of ordinary differential equations. Jafari transform belongs to the class of Laplace transform and is considered a generalization to integral transforms such as Laplace, Elzaki, Sumudu, G\_transforms, Aboodh, Pourreza, etc. Jafari transform does not need a large computational work as the previous integral transforms. For the Jafari transform, we have studied some valuable properties and theories that have not been studied before. Such as the linearity property, scaling property, first and second shift properties, the transformation of periodic functions, Heaviside function, and the transformation of Dirac’s delta function, and so on. There is a mathematical model that describes the cell population dynamics in the colonic crypt and colorectal cancer. We have applied the Jafari transform for solving this model.

Sign in / Sign up

Export Citation Format

Share Document