Numerical Investigation of the Nonlinear Coupled Fractional Massive Thirring Equation Using Two‐Scale Approach

Abstract

In this paper, we investigate the numerical solution of the coupled fractional massive Thirring equation with the aid of He’s fractional complex transform (FCT). This study plays a significant aspect in the field of quantum physics, weakly nonlinear thrilling waves, and nonlinear optics. The main advantage of FCT is that it converts the fractional differential equation into its traditional parts and is also capable to handle the fractional order, whereas the homotopy perturbation method (HPM) is employed to tackle the nonlinear terms in the coupled fractional massive Thirring equation. An example is illustrated to present the efficiency and validity of the two-scale theory. The solutions are obtained in the form of series with simple and easy computations which confirm that the present approach is good in agreement and is easy to implement for such type of complex systems in science and engineering.

Approximate solution of Newell-Whitehead-Segel model with time-fractional derivative

“…The study of FC has been applied to various fields such as electrodynamics, the study of chaos, and optical science [ 1 – 3 ]. Numerous scholars and scientists have contributed to the significance of FC in different branches of sciences such as fractional-order two-dimensional Helmholtz equations [ 4 ], nonlinear coupled fractional massive thirring equation [ 5 ], Klein-Gordon equation [ 6 ], time-fractional Navier-Stokes equation [ 7 ], nonlinear shock wave equations with fractional order [ 8 ], fractional Fokas Lenells equation [ 9 ], fractional acoustic waves model [ 10 ], Korteweg-de Vries (KdV) equation [ 11 ], fractional study of the non-linear burgers’ equations [ 12 ] and many other nonlinear system such as high order uncertain nonlinear systems [ 13 ], nonlinear networked control systems [ 14 ], radial basis function neural network model [ 15 ], Bayesian network analysis [ 16 ], reaction-diffusion system [ 17 ] and Keller-Segel model [ 18 ]. Finding the exact solution of these nonlinear fractal models is still challenging thus analytical and numerical schemes are the most suitable approaches to derive the fractal solution of these nonlinear models.…”