Open AccessJournal Article
Introducing and Analysing Deeper Sumudu Properties
TLDR
This paper attempts to be the single most comprehensive source about the Sumudu Transform properties, up to date.Abstract:
The Sumudu Transform, herein simply referred to as the Sumudu, was previously firmly established by the author et al.[2003/2005] as the theoretical dual to the Laplace Transform, where from the Laplace-Sumudu Duality (LSD). In fact, due to its units and scale preserving properties, in many instances, the Sumudu may be preferred to its dual for solving problems in engineering mathematics, without leaving the initial argument domain. Many fundamental Sumudu properties were presented in the literature, by this author and others. Aside from reestablishing these with alternative tools, essentially deeper Sumudu properties and connections are analyzed, and new results are presented. As such, this paper attempts to be the single most comprehensive source about the Sumudu Transform properties, up to date.read more
Citations
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The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method
TL;DR: In this paper, the Sumudu transform was used to solve nonhomogeneous fractional ordinary differential equations (FODEs) and then the solutions were used to form two-dimensional (2D) graphs.
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Application of He's Homotopy Perturbation Method to Sumudu Transform
TL;DR: In this article, an application of He's homotopy perturbation method is proposed to compute Sumudu transform, in contrast of usual methods which need integration, requires simple differentiation.
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A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow
TL;DR: The pivotal proposal of this work is to present a reliable algorithm based on the local fractional homotopy perturbation Sumudu transform technique for solving a local fractionsal Tricomi equation occurring in fractal transonic flow.
Journal Article
Applications of the Sumudu transform to fractional differential equations
TL;DR: In this paper, a table of a hundred instances of basic and special functions fractional integrals sumudi is provided, and some Sumudu properties are either generalized, or newly established.
Journal Article
Theory of Natural Transform
TL;DR: In this paper, the Natural transform is derived from the Fourier Integral and it converges to Laplace and Sumudu transform, it is shown it to the theoretical dual of Laplace, and it is proved Natural-multiple shift theorems, Bromwich contour integral and Heviside's Expansion formula for Inverse Natural transform.
References
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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.
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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.
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Analytical investigations of the sumudu transform and applications to integral production equations
TL;DR: 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.
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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.
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Sumudu transform and the solution of integral equation of convolution type
TL;DR: The convolution theorem for the Sumudu transform of a function which can be expressed as a polynomial or a convergent infinite series is proved and its applicability demonstrated in solving convolution type integral equations as mentioned in this paper.