scholarly journals A new analytical modelling for fractional telegraph equation via Elzaki transform

2015 ◽  
Vol 11 (9) ◽  
pp. 5617-5625
Author(s):  
Huan Li
Keyword(s):  
Numerical Solutions ◽  
Simple Algorithm ◽  
Telegraph Equation ◽  
Analytical Modelling ◽  
Transform Method ◽  
Fractional Telegraph Equation ◽  
Homotopy Analysis ◽  
Accuracy And Stability

The main aim of this paper is to propose a new and simple algorithm for space-fractional telegraph equation, namely new fractional homotopy analysis transform method (FHATM). The fractional homotopy analysis transform method is an innovative adjustment in Elzaki transform algorithm (ETA) and makes the calculation much sim-pler. The numerical solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. Finally, several numerical ex-amples are given to illustrate the accuracy and stability of this method.

Fractional modelling arising in unidirectional propagation of long waves in dispersive media

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Sunil Kumar ◽  
Devendra Kumar ◽  
Jagdev Singh
Keyword(s):  
Numerical Solutions ◽  
Simple Algorithm ◽  
Nonlinear Problems ◽  
Convergent Series ◽  
Dispersive Media ◽  
Transform Method ◽  
Adomian Polynomials ◽  
Modified Method ◽  
Homotopy Analysis ◽  
The Laplace Transform

AbstractThe purpose of this paper is to propose a modified and simple algorithm for fractional modelling arising in unidirectional propagation of long wave in dispersive media by using the fractional homotopy analysis transform method (FHATM). This modified method is an innovative adjustment in the Laplace transform algorithm (LTA) and makes the calculation much simpler. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method. This modified method yields an analytical and approximate solution in terms of a rapidly convergent series with easily computable terms. The numerical solutions obtained by the proposed algorithm indicate that the approach is easy to implement and computationally very attractive. Comparing our solution with the existing ones, we note an excellent agreement.

scholarly journals Collocation solutions for the time fractional telegraph equation using cubic B-spline finite elements

2019 ◽  
Vol 57 (2) ◽  
pp. 131-144
Author(s):  
Orkun Tasbozan ◽  
Alaattin Esen
Keyword(s):  
Finite Elements ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Telegraph Equation ◽  
Numerical Results ◽  
Fractional Partial Differential Equations ◽  
Spline Collocation ◽  
B Spline ◽  
Fractional Telegraph Equation

Abstract In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional derivatives have been considered in the Caputo forms. The L1and L2 formulae are used to discretize the Caputo fractional derivative with respect to time. Some examples have been given for determining the accuracy of the regarded method. Obtained numerical results are compared with exact solutions arising in the literature and the error norms L 2 and L ∞ have been computed. In addition, graphical representations of numerical results are given. The obtained results show that the considered method is effective and applicable for obtaining the numerical results of nonlinear fractional partial differential equations (FPDEs).

scholarly journals Conformable Sumudu Transform of Space-Time Fractional Telegraph Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Amjad E. Hamza ◽  
Mohamed Z. Mohamed ◽  
Eltaib M. Abd Elmohmoud ◽  
M. Magzoub
Keyword(s):  
Numerical Model ◽  
Numerical Solutions ◽  
Transformation Method ◽  
Telegraph Equation ◽  
Space Time ◽  
Science And Engineering ◽  
Fractional Equations ◽  
Fractional Telegraph Equation ◽  
Presentation Method ◽  
Sumudu Transform

This paper intends to obtain accurate and convergent numerical solutions of linear space-time matching telegraph fractional equations by means of a double Sumudu matching transformation method. Moreover, the numerical model is equipped to explain the work, the accuracy of the work, and sobriety in its presentation method, and as a result, the proposed method shows an effective and convenient way, to employ proven problems in science and engineering.

The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation

2014 ◽  
Vol 24 (8) ◽  
pp. 1636-1659 ◽  
Author(s):  
Akbar Mohebbi ◽  
Mostafa Abbaszadeh ◽  
Mehdi Dehghan
Keyword(s):  
Radial Basis Functions ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Telegraph Equation ◽  
Basis Functions ◽  
Content Type ◽  
Fractional Telegraph Equation ◽  
Radial Basis ◽  
Collocation Approach ◽  
Derivatives Of

Purpose – The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation. Design/methodology/approach – In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives. Findings – The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy. Originality/value – The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

Analytical method for space-fractional telegraph equation by homotopy perturbation transform method

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Amit Prakash
Keyword(s):  
Laplace Transform ◽  
Present Article ◽  
Analytical Method ◽  
Telegraph Equation ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractional Telegraph Equation

AbstractThe object of the present article is to study spacefractional telegraph equation by fractional Homotopy perturbation transform method (FHPTM). The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm. Three test examples are presented to show the efficiency of the proposed technique.

Numerical Computation of a Fractional Model of Differential-Difference Equation

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Difference Problem ◽  
Transform Method ◽  
Fractional Model ◽  
Analytical And Numerical Solutions ◽  
Adomian Decomposition ◽  
Homotopy Analysis ◽  
Sumudu Transform

In the present article, we apply a numerical scheme, namely, homotopy analysis Sumudu transform algorithm, to derive the analytical and numerical solutions of a nonlinear fractional differential-difference problem occurring in nanohydrodynamics, heat conduction in nanoscale, and electronic current that flows through carbon nanotubes. The homotopy analysis Sumudu transform method (HASTM) is an inventive coupling of Sumudu transform algorithm and homotopy analysis technique that makes the calculation very easy. The fractional model is also handled with the aid of Adomian decomposition method (ADM). The numerical results derived with the help of HASTM and ADM are approximately same, so this scheme may be considered an alternative and well-organized technique for attaining analytical and numerical solutions of fractional model of discontinued problems. The analytical and numerical results derived by the application of the proposed technique reveal that the scheme is very effective, accurate, flexible, easy to apply, and computationally very appropriate for such type of fractional problems arising in physics, chemistry, biology, engineering, finance, etc.

Numerical approximation of Newell-Whitehead-Segel equation of fractional order

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Devendra Kumar ◽  
Ram Prakash Sharma
Keyword(s):  
Fractional Order ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Analysis Method ◽  
Transform Method ◽  
Analysis Technique ◽  
Homotopy Analysis ◽  
Sumudu Transform ◽  
Linear Differential ◽  
User Friendly

AbstractThe aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order.

scholarly journals Generalized Differential Transform Method to Space-Time Fractional Telegraph Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Mridula Garg ◽  
Pratibha Manohar ◽  
Shyam L. Kalla
Keyword(s):  
Closed Form ◽  
Fractional Derivatives ◽  
Telegraph Equation ◽  
Space Time ◽  
Differential Transform Method ◽  
Transform Method ◽  
Space And Time ◽  
Fractional Telegraph Equation ◽  
Differential Transform ◽  
Generalized Differential

We use generalized differential transform method (GDTM) to derive the solution of space-time fractional telegraph equation in closed form. The space and time fractional derivatives are considered in Caputo sense and the solution is obtained in terms of Mittag-Leffler functions.

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