Journal ArticleDOI
Further Properties of the Sumudu Transform and Its Applications.
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TLDR
In this paper, the Sumudu transform of a special function f (t) with a corresponding sumudu transformation F (u) has been studied and the effect of shifting the parameter t in the function f(t) by τ on the transform F(u) is analyzed.Abstract:
This note discusses the general properties of the Sumudu transform and the Sumudu transform of special functions. For any function f (t) with corresponding Sumudu transform F (u), the effect of shifting the parameter t in f (t) by τ on the Sumudu transform F (u) is found. Also obtained are the effect of the multiplication of any function f (t) by a power of t and the division of the function f (t) by t on the Sumudu transform F (u). For any periodic function f (t) with periodicity T > 0 the Sumudu transform is easily derived. Illustrations are provided with Abel's integral equation, an integro-differential equation, a dynamic system with delayed time signals and a differential dynamic system.read more
Citations
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Book
Advanced Calculus I
TL;DR: It is quite impossible to include in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages, so it becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer.
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
On the applications of Laplace and Sumudu transforms
TL;DR: An example of the double Sumudu transform is provided in order to solve the wave equation in one dimension which is having singularity at initial conditions.
Journal ArticleDOI
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.
Journal Article
Introducing and Analysing Deeper Sumudu Properties
TL;DR: This paper attempts to be the single most comprehensive source about the Sumudu Transform properties, up to date.
References
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Book
Advanced Calculus I
TL;DR: It is quite impossible to include in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages, so it becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer.
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.
Book
Mathematical methods for science students
TL;DR: The first two years of a typical University or Polytechnic course, and it is developed assuming only an elementary knowledge of pre-University mathematics, can be found in this paper.
Journal ArticleDOI
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.