Analytical investigations of the sumudu transform and applications to integral production equations
TLDR
In this article, the Sumudu transform was used to solve an integral production-depreciation problem, where the Laplace transform was applied to solve the problem without resorting to a new frequency domain.Abstract:
The Sumudu transform, whose fundamental properties are
presented in this paper, is little known and not widely used
However, being the theoretical dual to the Laplace
transform, the Sumudu transform rivals it in problem solving
Having scale and unit-preserving properties, the Sumudu transform
may be used to solve problems without resorting to a new
frequency domain Here, we use it to solve an integral
production-depreciation problemread more
Citations
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Journal ArticleDOI
Sumudu transform fundamental properties investigations and applications.
TL;DR: In this paper, the Sumudu transform is used to solve problems without resorting to a new frequency domain, which is the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving.
Journal ArticleDOI
A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control
TL;DR: In this article, the authors used a box model to model hearing loss in children caused by the mumps virus, and since the fractional-order derivative retains the effect of system memory, they used the Caputo-Fabrizio fractional derivative in this modeling.
Journal ArticleDOI
Analysis of the model of HIV-1 infection of CD4+$CD4^{+}$ T-cell with a new approach of fractional derivative
TL;DR: In this paper, a new version for the mathematical model of HIV was proposed by using the fractional Caputo-Fabrizio derivative, and the existence and uniqueness of the solution for the model by using fixed point theory.
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An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma
TL;DR: In this paper, a coupling of homotopy perturbation technique and sumudu transform is presented for studying the nonlinear behavior of plasma system and highlight the important points.
Journal ArticleDOI
A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
TL;DR: A fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative is presented and it is proved the existence of a unique solution and the stability of the iteration approach by using fixed point theory.
References
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Book
Advanced Engineering Mathematics
TL;DR: This book discusses ODEs, Partial Differential Equations, Fourier Series, Integrals, and Transforms, and Numerics for ODE's and PDE's, as well as numerical analysis and potential theory, and more.
Journal ArticleDOI
Advanced Engineering Mathematics. ByErwin Kreyszig. Pp. xx, 899. 68s. (Wiley.)
Sumudu Transform - a New Integral Transform to Solve Differential Equations and Control Engineering Problems
TL;DR: u and F (u) are no longer dummies but can be treated as replicas of t and f (t) and can be expressed using same respective units, and therefore one can check the consistency of units of a differential equation even after the Sumudu transform.
Journal ArticleDOI
Sumudu transform: a new integral transform to solve differential equations and control engineering problems
TL;DR: The Sumudu transform as discussed by the authors is a new integral transform that makes its visualization easier and has many interesting properties, such as: (1) the differentiation and integration in the tdomain is equivalent to division and multiplication of the transformed function F(u) by uin the udomain.