On Sumudu Transform and System of Differential Equations

Kılıçman, Adem; Eltayeb, Hassan; Agarwal, Ravi P.

doi:10.1155/2010/598702

Cited by 44 publications

(21 citation statements)

References 4 publications

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“…Recently, this transform is applied to solve the system of differential equations and partial differential equations; see Kilicman et al in [19] and [20].…”

Section: Sumudu Transformmentioning

confidence: 99%

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A Study on Temperature-Distribution and Fin Efficiency of Convective Straight Fins With Temperature Dependent Thermal Conductivity of Fractional Order Energy Balance Equation by Using Adomian Decomposition Sumudu Transform Method

Patel¹,

Meher²

2016

Int. J. of Pure and Appl. Math.

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In this study, an attempt has been made to fractionalize the governing energy balance equation and Adomian decomposition Sumudu transform method (ADSTM) is used to solve the nonlinear fractional order energy balance equation to find the temperature distribution and to check the efficiency of convective straight fin with temperature dependent thermal conductivity. The thermal conductivity of the fin material is assumed as a linear function of temperature to find the temperature distribution for different values of thermal conductivity and thermo-geometric fin parameters for fractional as well as for integer order energy balance equation. Finally, the obtained ADSTM results has been compared with Variational Iteration Method (VIM) (Coskun et al., 2008) and Numerical method to check the accuracy of the purposed method.

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“…Recently, this transform is applied to solve the system of differential equations and partial differential equations; see Kilicman et al in [19] and [20].…”

Section: Sumudu Transformmentioning

confidence: 99%

“…Now, applying sumudu transform and then inverse sumudu transform on both sides of equation (19), it obtains…”

Section: Application Of Adstm For Finding Fin Temperature In Fractionmentioning

confidence: 99%

A Study on Temperature-Distribution and Fin Efficiency of Convective Straight Fins With Temperature Dependent Thermal Conductivity of Fractional Order Energy Balance Equation by Using Adomian Decomposition Sumudu Transform Method

Patel¹,

Meher²

2016

Int. J. of Pure and Appl. Math.

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“…Sumudu transform was first introduced by [30] and some of its applications were given by [2,14,20,22]. For more information and features regarding Sumudu transform we refer to [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

On double Natural transform and its applications

Kılıçman¹,

Omran²

2017

J. Nonlinear Sci. Appl.

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In this work, we generalize the concept of one dimensional Natural transform to two dimensional Natural transform namely, double Natural transform and some of its properties are given. We also set a relation between double Natural transform and double Laplace, double Sumudu transforms. Further the convolution theorem with a proof is investigated with some details. Double Natural transform is applied to get the solutions of some general linear telegraphs, wave and partial integro-differential equations.

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“…where the variables u and υ are the natural transform variables which indeed strictly converge to the Sumudu transform [3,18] …”

Section: Introductionmentioning

confidence: 99%

On the Application of Natural Transforms

Al‐Omari¹

2013

Int. J. of Pure and Appl. Math.

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In many papers, integral transforms have been introduced and found their application in solving certain boundary value problems. Indeed, as reference [1] shows, the natural transform is closely connected with Laplace and Sumudu transforms. In this paper we employ this transform to solving initial value problems of constant coefficients. Further, we discuss this transform on spaces of generalized functions. The distributional face of the natural transform is obtained as an analytic distribution. Whereas, the natural transform of a Boehmian is introduced by its limit in the distributional sense. More results are also established.

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On Sumudu Transform and System of Differential Equations

Abstract: The regular system of differential equations with convolution terms solved by Sumudu transform.

Cited by 44 publications

References 4 publications

A Study on Temperature-Distribution and Fin Efficiency of Convective Straight Fins With Temperature Dependent Thermal Conductivity of Fractional Order Energy Balance Equation by Using Adomian Decomposition Sumudu Transform Method

A Study on Temperature-Distribution and Fin Efficiency of Convective Straight Fins With Temperature Dependent Thermal Conductivity of Fractional Order Energy Balance Equation by Using Adomian Decomposition Sumudu Transform Method

On double Natural transform and its applications

On the Application of Natural Transforms

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