Sumudu transform and the solution of integral equations of convolution type

Aṣiru, Muniru A.

doi:10.1080/002073901317147870

Cited by 90 publications

(57 citation statements)

References 3 publications

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“…Once more, Watugala's work was followed by Weerakoon [14] introducing a complex inversion formula for the Sumudu transform (see Theorem 3.1 in Section 3). The relatively recent sequence [1][2][3], indicated how to use the transform to solve integrodifferential equations, with emphasis on dynamic systems. Watugala [12] extended the transform to two variables with emphasis on solutions to partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Sumudu transform fundamental properties investigations andapplications

Belgacem

Karaballi

2006

International Journal of Stochastic Analysis

254

165

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The Sumudu transform, whose fundamental properties are presented in this paper, is still not widely known, nor used. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. In 2003, Belgacem et al. have shown it to be the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving. Here, using the Laplace-Sumudu duality (LSD), we avail the reader with a complex formulation for the inverse Sumudu transform. Furthermore, we generalize all existing Sumudu differentiation, integration, and convolution theorems in the existing literature. We also generalize all existing Sumudu shifting theorems, and introduce new results and recurrence results, in this regard. Moreover, we use the Sumudu shift theorems to introduce a paradigm shift into the thinking of transform usage, with respect to solving differential equations, that may be unique to this transform due to its unit-preserving properties. Finally, we provide a large and more comprehensive list of Sumudu transforms of functions than is available in the literature.

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Section: Introductionmentioning

confidence: 99%

Sumudu transform fundamental properties investigations andapplications

Belgacem

Karaballi

2006

International Journal of Stochastic Analysis

254

165

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“…For more information and properties of Sumudu transform and its derivatives, [14][15][16][17][18][19]. Actually one can simply prove that there is a big connection between double Sumudu and double Laplace transforms.…”

Section: Sumudu Transformmentioning

confidence: 99%

European Option Pricing of Fractional Black-Scholes Model Using Sumudu Transform and its Derivatives

Khan¹,

Ansari²

2016

GLM

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“…For more details about Sumudu transform, see ( [1][2][3][4][5][6][7][8][9]). The Sumudu transform over the set functions…”

Section: Introductionmentioning

confidence: 99%

On Image Formulae Leading to Fractional Kinetic Equations Solutions via Sumudu Generalized k-Bessel Functions

Nisar¹,

Ms²,

Belgacem³

2017

Preprint

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Abstract. Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal [24]. In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the process, Important special cases are then revealed, and analyzed.

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Sumudu transform and the solution of integral equations of convolution type

Cited by 90 publications

References 3 publications

Sumudu transform fundamental properties investigations andapplications

Sumudu transform fundamental properties investigations andapplications

European Option Pricing of Fractional Black-Scholes Model Using Sumudu Transform and its Derivatives

On Image Formulae Leading to Fractional Kinetic Equations Solutions via Sumudu Generalized k-Bessel Functions

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