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.

scholarly journals On the Solution of Generalized Space Time Fractional Telegraph Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Badr S. Alkahtani ◽  
Vartika Gulati ◽  
Pranay Goswami
Keyword(s):  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Telegraph Equation ◽  
Space Time ◽  
New Technique ◽  
Variational Iteration ◽  
Fractional Telegraph Equation ◽  
Sumudu Transform

We present the solution of generalized space time fractional telegraph equation by using Sumudu variational iteration method which is the combination of variational iteration method and Sumudu transform. We tried to overcome the difficulties in finding the value of Lagrange multiplier by this new technique.

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 Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique

2021 ◽  
Author(s):  
Ummay Sadia ◽  
Mohammad Asif Arefin ◽  
Mustafa Inc ◽  
M. Hafiz Uddin
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Traveling Wave ◽  
Telegraph Equation ◽  
Space Time ◽  
Nonlinear Evolution Equations ◽  
Communication Line ◽  
Third Order ◽  
Wave Solutions ◽  
Fractional Telegraph Equation

Abstract The space-time fractional telegraph equation and the space-time fractional modified third-order Kdv equations are significant molding equations in theoretic physics, mathematical physics, plasma physics also other fields of nonlinear sciences. The space time-fractional telegraph equation, which appears in the investigation of an electrical communication line and includes voltage in addition to current which is dependent on distance and time, is also applied to communication lines of wholly frequencies, together with direct current, as well as high-frequency conductors, audio frequency (such as telephone lines), and low frequency (for example cable television) used in the extension of pressure waves into the lessons of pulsatory blood movement among arteries also the one-dimensional haphazard movement of bugs towards an obstacle. The presence of chain rule and the derivative of composite functions allows the nonlinear fractional differential equations (NLFDEs) to translate into the ordinary differential equation employing wave alteration. To explore such categories of resolutions, the extended tanh-method is accomplished via Conformable fractional derivatives. A power sequence in tanh was originally used as an ansatz to provide analytical solutions of the traveling wave type of certain nonlinear evolution equations. To convert this problem to a standard differential equation, a partial complex transformation that has been summarized succinctly is utilized correctly thus, with all of the free parameters, numerous exact logical arrangements are required. The results are found as hyperbolic and rational functions involving parameters, when specific values are supplied to the parameters solitary wave solutions are formed from traveling wave solutions. The outcomes achieved in this study are king type, single soliton, double soliton, multiple solitons, bell shape, and other sorts of forms and we demonstrated that these solutions were validated through the Maple software. The proposed approach for solving nonlinear fractional partial differential equations has been developed to be operative, unpretentious, quick, and reliable to usage.

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.

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.

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