Solving Poisson’s Equations with fractional order using Haarwavelet

Youssef, I. K.; Dewaik, M. H. El

doi:10.21042/amns.2017.1.00023

Cited by 28 publications

(7 citation statements)

References 8 publications

(6 reference statements)

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“…Recently, studies on the solution of fractional differential equations have increased. There are several studies about fractional problems and their computational accuracy in the literature [4][5][6]. Since the exact solution for many of the fractional differential equations are not found, various methods have been developed to find approximate or numerical solutions.…”

Section: Introductionmentioning

confidence: 99%

A Crank-Nicolson Approximation for the time Fractional Burgers Equation

Önal

Esen

2020

Applied Mathematics and Nonlinear Sciences

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In the present manuscript, Crank Nicolson finite difference method is going to be applied to get the approximate solutions for the fractional Burgers equation. The fractional derivative used in this equation is going to be taken into consideration in the Caputo sense. The L1 type discretization formula is going to be applied to this equation. For checking the efficiency of proposed methods, the error norms L2 and L∞ have at the same time been calculated. Those newly got solutions using the presented method illustrate the easy usage and efficiency of the approach presented in this manuscript.

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Section: Introductionmentioning

confidence: 99%

A Crank-Nicolson Approximation for the time Fractional Burgers Equation

Önal

Esen

2020

Applied Mathematics and Nonlinear Sciences

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“…Differential equations of the fractional order have a wide spectrum of applications, since they are often used to model problems in fluid dynamics, finance, biology, physics, engineering, etc. However, most of the exact methods of solution of the considered problems (see [1][2][3][4][5][6][7][8][9][10][11]) in the nonlinear case of differential equations and their systems are not applicable.…”

Section: Introductionmentioning

confidence: 99%

On One Interpolation Type Fractional Boundary-Value Problem

Marynets

2020

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We present some new results on the approximation of solutions of a special type of fractional boundary-value problem. The focus of our research is a system of three fractional differential equations of the mixed order, subjected to the so-called “interpolation” type boundary restrictions. Under certain conditions, the aforementioned problem is simplified via a proper parametrization technique, and with the help of the numerical-analytic method, the approximate solutions are constructed.

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“…Several problems of physical nature are central to, and crux of fractional differential equation. Recently many researchers have focused on techniques and methods for solving fractional differential equations [4][5][6][7][8][9][10]. In essence, fractional calculus has been deployed for fluid dynamics [11], bio engineering [12], electromagnetism [13], modeling the transfer of heat in heterogeneous media [14] and anomalous diffusion [15,16].…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method

et al. 2019

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In this study, we present a novel numerical scheme for the approximate solutions of linear as well as non-linear ordinary differential equations of fractional order with boundary conditions. This method combines Cosine and Sine (CAS) wavelets together with Green function, called Green-CAS method. The method simplifies the existing CAS wavelet method and does not require conventional operational matrices of integration for certain cases. Quasilinearization technique is used to transform non-linear fractional differential equations to linear equations and then Green-CAS method is applied. Furthermore, the proposed method has also been analyzed for convergence, particularly in the context of error analysis. Sufficient conditions for the existence of unique solutions are established for the boundary value problem under consideration. Moreover, to elaborate the effectiveness and accuracy of the proposed method, results of essential numerical applications have also been documented in graphical as well as tabular form.

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Solving Poisson’s Equations with fractional order using Haarwavelet

Cited by 28 publications

References 8 publications

A Crank-Nicolson Approximation for the time Fractional Burgers Equation

A Crank-Nicolson Approximation for the time Fractional Burgers Equation

On One Interpolation Type Fractional Boundary-Value Problem

Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method

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