Wave Effects of the Fractional Shallow Water Equation and the Fractional Optical Fiber Equation - Phoosree, Sirasrete; Thadee, Weerachai (Frontiers in Applied Mathematics and Statistics, 2022)
The nonlinear space-time fractional Estevez-Mansfield-Clarkson (EMC) equation and the nonlinear space-time fractional Ablowitz-Kaup-Newell-Segur (AKNS) equation showed the motion of waves in the shallow water equation and the optical fiber equation, respectively. The process used to solve these equations is transform the nonlinear fractional partial differential equations into the nonlinear ordinary differential equations by using the Jumarie’s Riemann-Liouville derivative and setting the solution in the finite series combined the simple equation (SE) method with Bernoulli equation. The new traveling wave solutions were the exponential functions resulting in the physical wave effects are produced in the form of kink waves and represented by the two-dimensional graph, three-dimensional graph and contour graph. In addition, the comparison of the solutions revealed that the new solutions have a more convenient and easier format.