An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations

Izaz Ali,Muhammad Arif,Poom Kumam,Umar Farooq,Dumitru Baleanu,Hassan Khan

doi:10.1109/access.2020.2970242

Abstract

In the present research article, a modified analytical method is applied to solve time-fractional telegraph equations. The Caputo-operator is used to express the derivative of fractional-order. The present method is the combination of two well-known methods namely Mohan transformation method and Adomian decomposition method. The validity of the proposed technique is confirmed through illustrative examples. It is observed that the obtained solutions have strong contact with the exact solution of the examples. Moreover, it is investigated that the present method has the desired degree of accuracy and provided the graphs closed form solutions of all targeted examples. The graphs have verified the convergence analysis of fractional-order solutions to integer-order solution. In conclusion, the suggested method is simple, straightforward and an effective technique to solve fractional-order partial differential equations.

Highlights

The fractional calculus (F.C) was created in 1695, with a problem about the value of the half-order derivative
A specific class in the form of hyperbolic partial differential equations (PDEs), which depict the vibrations within objects and the phenomena of wave propagation in medium, is known as telegraph equation [22]
IMPLEMENTATION OF THE M.T DECOMPOSITION METHOD we considered the following telegraph equation

Summary

INTRODUCTION

The fractional calculus (F.C) was created in 1695, with a problem about the value of the half-order derivative. Mathematics [5], fractional-order telegraph equations [6], third-Order dispersive fractional partial differential equations (PDEs) [7], KdV-Kuramoto-Burger equation of fractionalorder [8], fractal flow of traffic [9], Drinfeld-Sokolov-Wilson equation [10], time-fractional sub-diffusion and anomalous equations [11], heat equations of fractional-order [9], [12], fractional option pricing problems [13], [14], fractional coupled viscous Burgers’ equation [15], hepatitis B virus fractional dynamic model [16], fractional model for tuberculosis [17], pine wilt disease fractional order model [18], fractional diabetes model [19], fractional-order Navier-Stokes equations [20], [21] etc. The obtained results have confirmed the importance of M.T to handle Abel’s solution [48]

PRELIMINARY CONCEPTS

APPLICATIONS AND DISCUSSION

RESULTS AND DISCUSSION

CONCLUSION