Dianchen Lu , Shenghui Ye (2019). Optical Solitary Wave Solutions of the Space-Time Fractional Modified Equal-Width Equation and their Applications. International Journal of Mathematical Research, 8(1): 1-20. DOI: 10.18488/journal.24.2019.81.1.20
The space-time fractional modified equal-width equation is a class of fractional partial differential equations which have been used widely in nonlinear optics, solid state physics. In this article, the improved (G/G)- expansion method has been proposed to construct more new exact solutions of the space-time fractional modified equal-width equation in the sense of modified Riemann-Liouville derivative. The traveling wave transform has been extended to convert the fractional order partial differential equation into an ordinary differential equation. In the end, three families of exact analytical solutions are obtained and expressed them in terms of the hyperbolic, trigonometric, and rational functions with arbitrary parameters, Which reveals that the improved (G/G)-expansion method is very effective and reliable for solving fractional order partial differential equations. Moreover, the graphical representation of solution is given at different values of a, Which is helpful for people to better study the physical structure of solutions and to analyze the nonlinear optical problems in nonlinear systems.
This study contributes in the existing literature through the improved (G/G) -expansion method. By applying this method, more new exact solutions of the space-time fractional modified equal-width equation are obtained. The resulting solutions are useful for analyzing nonlinear optics problems.