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

Mostafa M A Khater,Jung Rye Lee,Choonkil Park,Raghda A M Attia,Mohamed S Mohamed

doi:10.1186/s13662-021-03387-9

Abstract

The 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.

Highlights

The nonlinearity has been used in distinct fields such as the neural network [2], infectious disease epidemiology [3], plasma physics [4], thermodynamics [5], optic physics [6], population ecology [7], biology and mechanics of fluids [8, 9]
This paper investigates the fractional nonlinear telegraph equation that is used to describe the transmission of the voltage standard [29]
The numerical solutions of the fractional nonlinear telegraph equation are investigated through five recent schemes based on the obtained analytical solutions in [1]

Summary

Introduction

The nonlinearity has been used in distinct fields such as the neural network [2], infectious disease epidemiology [3], plasma physics [4], thermodynamics [5], optic physics [6], population ecology [7], biology and mechanics of fluids [8, 9]. Nowadays, based on the integer-order derivative’s failure to show the nonlocal property of the investigated model, many nonlinear phenomena have been formulated in fractional forms [21,22,23]. Khater et al Advances in Difference Equations [24,25,26], to transform the fractional nonlinear partial differential equations to nonlinear ordinary differential ones [27, 28] In this context, this paper investigates the fractional nonlinear telegraph equation that is used to describe the transmission of the voltage standard [29]. This paper investigates the fractional nonlinear telegraph equation that is used to describe the transmission of the voltage standard [29] This mathematical model is considered as a primary icon in the electromagnetic waves’ area.

Approximate analysis

Results and discussion

Conclusion