Dispersive traveling wave solutions to the space–time fractional equal-width dynamical equation and its applications

2018 ◽  
Vol 50 (3) ◽  
Author(s):  
Kalim U. Tariq ◽  
Aly R. Seadawy ◽  
Muhammad Younis ◽  
S. T. R. Rizvi
Keyword(s):  
Traveling Wave ◽  
Dynamical Equation ◽  
Traveling Wave Solutions ◽  
Space Time ◽  
Wave Solutions

scholarly journals Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Choonkil Park ◽  
Jung Rye Lee ◽  
Mohamed S. Mohamed ◽  
Raghda A. M. Attia
Keyword(s):  
Numerical Simulations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Approximate Solutions ◽  
Telegraph Equation ◽  
Space Time ◽  
Numerical Techniques ◽  
B Spline ◽  
Wave Solutions ◽  
Adomian Decomposition

AbstractThe accuracy of analytical obtained solutions of the fractional nonlinear space–time telegraph equation that has been constructed in (Hamed and Khater in J. Math., 2020) is checked through five recent semi-analytical and numerical techniques. Adomian decomposition (AD), El Kalla (EK), cubic B-spline (CBS), extended cubic B-spline (ECBS), and exponential cubic B-spline (ExCBS) schemes are used to explain the matching between analytical and approximate solutions, which shows the accuracy of constructed traveling wave solutions. In 1880, Oliver Heaviside derived the considered model to describe the cutting-edge or voltage of an electrified transmission. The matching between solutions has been explained by plotting them in some different sketches.

scholarly journals Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Dianchen Lu ◽  
Chen Yue ◽  
Muhammad Arshad
Keyword(s):  
Wave Propagation ◽  
Traveling Wave ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
One Dimensional ◽  
Wave Solutions ◽  
Fifth Order

The Korteweg-de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice. In this article, the generalizedexp⁡(-Φ(ξ))-expansion method is proposed to construct exact solutions of space-time fractional generalized fifth-order KdV equation with Jumarie’s modified Riemann-Liouville derivatives. At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.

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