Numerical Analysis of the Fractional-Order Telegraph Equations

Nehad Ali Shah,Fatemah Mofarreh,Omar Fouad Azhar,Jeevan Kafle,Muhammad Naeem

doi:10.1155/2021/2295804

Abstract

This paper studied the fractional-order telegraph equations via the natural transform decomposition method with nonsingular kernel derivatives. The fractional result considered in the Caputo-Fabrizio derivative is Caputo sense. Currently, the communication system plays a vital role in a global society. High-frequency telecommunications continuously receive significant attention in the industry due to a slew of radiofrequency and microwave communication networks. These technologies use transmission media to move information-carrying signals from one location to another. We used natural transformation on fractional telegraph equations followed by inverse natural transformation to achieve the solution of the equation. To validate the technique, we have considered a few problems and compared them with the exact solutions.

Highlights

The telegraph equation is usually applied in signal analysis for electrical signal propagation and transmission reactiondiffusion modeling in several areas of science
We have investigated the telegraph equations through natural transformation with the Caputo-Fabrizio derivative
It is shown that the fractional-order results were convergent to the actual result in the examples, as the fractional order approached the integer order

Summary

Introduction

The telegraph equation is usually applied in signal analysis for electrical signal propagation and transmission reactiondiffusion modeling in several areas of science. A wide range of microwave and radiofrequency communication systems continue to benefit from significant industry attention These technologies use media of communication to convey the signal from one place to another [1, 2]. The controlled medium can carry high-frequency and current waves, whereas electromagnetic waves in unguided media transmit a signal via radiofrequency and microwave channels, part or whole communication path. To maximize the guided communication system, power and signal losses must be determined or projected, as these losses exist in all scenarios To quantify these losses and eventually secure maximum output, some equations that can compute these losses must be developed. These equations appear in the fractional order rather than the integer order [3]

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