scholarly journals Analytical solution for a generalized space-time fractional telegraph equation

2013 ◽  
Vol 36 (14) ◽  
pp. 1813-1824 ◽  
Author(s):  
Ahmad Z. Fino ◽  
Hassan Ibrahim
Keyword(s):  
Analytical Solution ◽  
Telegraph Equation ◽  
Space Time ◽  
Fractional Telegraph Equation

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 A non-differentiable solution for the local fractional telegraph equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 225-231
Author(s):  
Jie Li ◽  
Ce Zhang ◽  
Weixing Liu ◽  
Yuzhu Zhang ◽  
Aimin Yang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Series Expansion ◽  
Expansion Method ◽  
Telegraph Equation ◽  
Differentiable Solution ◽  
Local Fractional Derivative ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
Series Expansion Method

In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

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.

scholarly journals Analytical Solution for the Time-Fractional Telegraph Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
F. Huang
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Boundary Problem ◽  
Fourier Transforms ◽  
Telegraph Equation ◽  
Green Functions ◽  
Laplace And Fourier Transforms ◽  
Sine Transform ◽  
Fractional Telegraph Equation ◽  
Bounded Space

We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variabletandx,respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.

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