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.

Numerical methods for differential algebraic equations

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 141-198 ◽  
Author(s):  
Roswitha März
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Image Position

Differential algebraic equations (DAE) are special implicit ordinary differential equations (ODE)where the partial Jacobian f′y(y, x, t) is singular for all values of its arguments.

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 Aboodh and Mahgoub Transform in Boundary Value Problems of System of Ordinary Differential Equations

2021 ◽  
pp. 67-75
Author(s):  
Dr. D. P. Patil
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Value ◽  
Integral Transforms

Integral transforms plays important role in solving differential equations and integral equations. In this paper we discuss application of Aboodh transform and Mahgoub transform in solving boundary value problem of system of ordinary differential equations and result shows that Aboodh transform and Mahgoub transform are closely connected.

scholarly journals On the Mohand Transform and Ordinary Differential Equations with Variable Coefficients

2020 ◽  
Vol 35 (1) ◽  
pp. 01-06
Author(s):  
Mohamed E. Attaweel ◽  
Haneen Almassry
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Integral Transform ◽  
Variable Coefficients ◽  
Sumudu Transforms ◽  
Differential And Integral Equations

The Mohand transform is a new integral transform introduced by Mohand M. Abdelrahim Mahgoub to facilitate the solution of differential and integral equations. In this article, a new integral transform, namely Mohand transform was applied to solve ordinary differential equations with variable coefficients by using the modified version of Laplace and Sumudu transforms.

scholarly journals A Robust Method for the Estimation of Kinetic Parameters for Systems Including Slow and Rapid Reactions—From Differential-Algebraic Model to Differential Model

Processes ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 1552
Author(s):  
Tapio Salmi ◽  
Esko Tirronen ◽  
Johan Wärnå ◽  
Jyri-Pekka Mikkola ◽  
Dmitry Murzin ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Kinetic Parameters ◽  
Algebraic Model ◽  
Algebraic Equations ◽  
Robust Method ◽  
Differential Model ◽  
Chemical Systems

Reliable estimation of kinetic parameters in chemical systems comprising both slow and rapid reaction steps and rapidly reacting intermediate species is a difficult differential-algebraic problem. Consequently, any conventional approach easily leads to serious convergence and stability problems during the parameter estimation. A robust method is proposed to surmount this dilemma: the system of ordinary differential equations and nonlinear algebraic equations is converted to ordinary differential equations, which are solved in-situ during the parameter estimation. The approach was illustrated with two generic examples and an example from green chemistry: synthesis of dimethyl carbonate from carbon dioxide and methanol.

Singularly perturbed ordinary differential equations with dynamic limits

1996 ◽  
Vol 126 (3) ◽  
pp. 541-569 ◽  
Author(s):  
Zvi Artstein ◽  
Alexander Vigodner
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Invariant Measures ◽  
Type Equation ◽  
Slow Motion ◽  
Algebraic Equations ◽  
Direct Integral ◽  
Limit Behaviour ◽  
Unique Invariant Measure ◽  
Fast Flow

Coupled slow and fast motions generated by ordinary differential equations are examined. The qualitative limit behaviour of the trajectories as the small parameter tends to zero is sought after. Invariant measures of the parametrised fast flow are employed to describe the limit behaviour, rather than algebraic equations which are used in the standard reduced order approach. In the case of a unique invariant measure for each parameter, the limit of the slow motion is governed by a chattering type equation. Without the uniqueness, the limit of the slow motion solves a differential inclusion. The fast flow, in turn, converges in a statistical sense to the direct integral, respectively the set-valued direct integral, of the invariant measures.

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