On double Natural transform and its applications

Kılıçman, Adem; Omran, Maryam

doi:10.22436/jnsa.010.04.36

Cited by 18 publications

(9 citation statements)

References 15 publications

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“…indicates double inverse Natural transform. The reader can read more about the Double Natural transform in [14].…”

Section: Properties Of Double Natural Transformmentioning

confidence: 99%

“…Where F p, s ; (u, v) and G p, s ; (u, v) are double Natural transform of the functions f (x, t) and (x, t) respectively. See [14].…”

Section: Example 2: [14]mentioning

confidence: 99%

“…The fundamental properties of double Natural transform of partial derivatives are given by the authors in [14], as follows:…”

Section: Example 2: [14]mentioning

confidence: 99%

“…In [15] the Natural Homotopy Perturbation Method has been successfully applied to linear and nonlinear Schrodinger equation. Recently double Natural transform has been applied to solve telegraph, wave and partial integro-differential equations see [14]. The aim of this paper is to propose an analytic solution of the singular one dimensional Boussinesq equation by using a modified double Natural decomposition method (MDNDM).…”

Section: Introductionmentioning

confidence: 99%

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Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

Eltayeb¹

2018

Filomat

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In this work, a combined form of the double Natural transform method with the Adomian decomposition method is developed for analytic treatment of the linear and nonlinear singular one dimensional Boussinesq equations. Two examples are provided to illustrate the simplicity and reliability of this method. Moreover, the results show that the proposed method is effective and is easy to implement for certain problems in science and engineering.

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“…indicates double inverse Natural transform. The reader can read more about the Double Natural transform in [14].…”

Section: Properties Of Double Natural Transformmentioning

confidence: 99%

“…Where F p, s ; (u, v) and G p, s ; (u, v) are double Natural transform of the functions f (x, t) and (x, t) respectively. See [14].…”

Section: Example 2: [14]mentioning

confidence: 99%

“…The fundamental properties of double Natural transform of partial derivatives are given by the authors in [14], as follows:…”

Section: Example 2: [14]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

Eltayeb¹

2018

Filomat

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“…The authors in [6], also introduced natural transform for solving differential equations. In [7], the authors extended the natural transform from one dimension to two dimensions and also, compared the double transform with Laplace and Sumudu transforms. The author in [8] introduced a polynomial integral transform PIT.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Integral Transform

Barnes

Sebil²,

Quaye³

2018

Eur. J. Pure Appl. Math.

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In this paper, the generalization of integral transform (GIT) of the func-tion G{f (t)} is introduced for solving both differential and interodif-ferential equations. This transform generalizes the integral transformswhich use exponential functions as their kernels and the integral trans-form with polynomial function as a kernel. The generalized integraltransform converts the differential equation in us domain (the trans-formed variables) and reconvert the result by its inverse operator. Inparticular, if u = 1, then the generalized integral transform coincideswith the Laplace transform and this result can be written in anotherform as the polynomial integral transform.

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A study of double general transform for solving fractional partial differential equations

Saadeh

Ghazal

Burqan

2023

Math Methods in App Sciences

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In this research, we introduce the basic properties of the single and double general transforms. New interesting results related to fractional operators in the sense of Caputo derivative are investigated and proved. In this study, the general double transformation is utilized to study the application on some special functions, such as the Mittag–Leffler function, and on the Caputo's fractional derivative of different and higher orders. Moreover, we establish new interesting formulas and prove some theories that can save efforts and time for researchers as they investigate the properties and applications of integral transformations on fractional operators. The results obtained in this research are tested by solving different types of fractional partial differential equations to obtain exact solutions. The outcomes of this article are valuable to researchers and mathematicians who are interested in the solving fractional partial differential equations via integral transforms, which are considered as important techniques to handle these equations.

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On double Natural transform and its applications

Cited by 18 publications

References 15 publications

Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

A Generalization of Integral Transform

A study of double general transform for solving fractional partial differential equations

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