Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Turut, Veyis; Güzel, Nuran

doi:10.1155/2013/746401

Cited by 30 publications

(16 citation statements)

References 17 publications

(32 reference statements)

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“…Odibat and Momani [3,4] applied several different types of methods to fractional PDEs and compared the results they obtained. On the other hand, several researchers [5][6][7][8][9][10][11][12][13][14][15][16][17] have applied the homotopy perturbation/analysis methods (HPM/HAM) and Adomian decomposition method (ADM) to solve different kinds of fractional ordinary differential equations (ODEs), fractional partial differential equations (ODEs), integral equations (IEs) and integro-differential equations (IDEs). Among them Javidi and Ahmad [18] proposed a numerical method which is based on the homotopy perturbation method and Laplace transform for fractional PDEs.…”

Section: Introductionmentioning

confidence: 99%

Novel solution methods for initial boundary value problems of fractional order with conformable differentiation

Yavuz

2017

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this work, we develop a formulation for the approximate-analytical solution of fractional partial differential equations (PDEs) by using conformable fractional derivative. Firstly, we redefine the conformable fractional Adomian decomposition method (CFADM) and conformable fractional modified homotopy perturbation method (CFMHPM). Then, we solve some initial boundary value problems (IBVP) by using the proposed methods, which can analytically solve the fractional partial differential equations (FPDE). In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of the IBVP. Also, we have found out that the proposed models are very efficient and powerful techniques in finding approximate solutions for the IBVP of fractional order in the conformable sense.

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Section: Introductionmentioning

confidence: 99%

Novel solution methods for initial boundary value problems of fractional order with conformable differentiation

Yavuz

2017

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…Fractional differential equations have been used to model problems in viscoelastic materials, fluid mechanics, biology, physics, finance, bioengineering and other areas of application [1,2,3,4,5,6]. There are many studies on Adomian decomposition method (ADM) which can evaluate the solutions of FPDEs.…”

Section: Introductionmentioning

confidence: 99%

Approximate-analytical solutions of cable equation using conformable fractional operator

Yaşkıran¹,

Yavuz²

2017

ntmsci

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Abstract:In the present work, we have introduced a new formulation for the approximate-analytical solution of the fractional onedimensional cable differential equation (FCE) by using the conformable fractional derivative. First of all, we have redefined Adomian decomposition method (CADM) and variational iteration method (CVIM) in the conformable sense. Then, we have solved by using the mentioned methods, which can analytically solve the fractional partial differential equations (FPDEs). In order to represent the efficiencies of these proposed methods, we have compared the numerical and exact solutions of the (FCE). Also, we have found out that the proposed models defined with the conformable derivative operator are very efficient and powerful techniques in finding approximate-analytical solutions for the cable equation of fractional order. In addition, the classical derivative and integral properties are recovered partially when the fractional term (alpha) is equal to one.

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“…In recent times, univariate and multivariate padé approximaton have been succesfully applied to various problems in physical and engineering sciences [1][2][3][4][5]. "Padé approximant represents a function by the ratio of two polynomials.…”

Section: Introductionmentioning

confidence: 99%

Rational approximations for solving cauchy problems

Turut¹,

Bayram²

2016

ntmsci

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In this letter, numerical solutions of Cauchy problems are considered by multivariate Padé approximations (MPA). Multivariate Padé approximations (MPA) were applied to power series solutions of Cauchy problems that solved by using He's variational iteration method (VIM). Then, numerical results obtained by using multivariate Padé approximations were compared with the exact solutions of Cauchy problems.

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Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Cited by 30 publications

References 17 publications

Novel solution methods for initial boundary value problems of fractional order with conformable differentiation

Novel solution methods for initial boundary value problems of fractional order with conformable differentiation

Approximate-analytical solutions of cable equation using conformable fractional operator

Rational approximations for solving cauchy problems

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