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The natural transform Decomposition Method for Solving Fractional Klein-Gordon Equation

Applied Mathematics 2023年第3期14卷 230-243页

作者： Mohamed Elbadri Department of Mathematics Faculty of Sciences and Arts Jouf University Tubarjal Saudi Arabia Department of Mathematics University of Gezira Wad Madani Sudan

In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.

关键词： natural transform Adomian Decomposition Method Fractional Klein-Gordon Equation

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natural transform for Solving Fractional Models

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Journal of Applied Mathematics and Physics 2015年第12期3卷 1633-1644页

作者： Ahmed Safwat Abdel-Rady Saad Zagloul Rida Anas Ahmed Mohamed Arafa Hamdy Ragab Abedl-Rahim Department of Mathematics Faculty of ScienceSouth Valley UniversityQenaEgypt Department of Mathematics and Computer Science Faculty of SciencePort Said UniversityPort SaidEgypt

In this paper, we present a novel technique to obtain approximate analytical solution of fractional physical models. The new technique is a combination of a domain decomposition method and natural transform method called a domain decomposition natural transform method (ADNTM). The fractional derivatives are considered in Caputo sense. To illustrate the power and reliability of the method some applications are provided.

关键词： Fractional Calculus natural transform A Domain Decomposition natural transform Method(ADNTM) Fokker-Planck Equation Schrodinger Equation Kelin-Gorden Equation

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A NEW INTEGRAL transform AND ITS APPLICATIONS

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Acta Mathematica Scientia 2015年第6期35卷 1386-1400页

作者： H.M.SRIVASTAVA 罗旻杰 R.K.RAINA Department of Mathematics and Statistics University of Victoria Department of Mathematics East China Normal University Department of Mathematics M.P.University of Agriculture and Technology

In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.

关键词： Laplace transform Sumudu transform natural transform H-function H- transform inversion formula Parseval-type relationship existence theorem Borel-Dzrbashjan transform Fubini's theorem Weierstrass's test Heaviside generalized function

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An efficient technique for two-dimensional fractional order biological population model

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第1期11卷 96-112页

作者： P.Veeresha D.G.Prakasha Department of Mathematics Karnatak University Dharwad 580003India Department of Mathematics Faculty of Science Davangere University ShivagangothriDavangere 577007India

In this paper,we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method(FNDM).The proposed method is a graceful blend of decomposition scheme with natural transform,and three examples are considered to validate and illustrate its *** nature of FNDM solution has been captured for distinct arbitrary *** order to illustrate the proficiency and reliability of the considered scheme,the numerical simulation has been *** obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.

关键词： Caputo fractional derivative decomposition method biological population model natural transform

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