Impact of Fractional Derivative and Brownian Motion on the Solutions of the Radhakrishnan-Kundu-Lakshmanan Equation.

The fractional-stochastic Radhakrishnan-Kundu-Lakshmanan equation (FSRKLE) is considered here. To attain new hyperbolic, elliptic, rational, and trigonometric stochastic-fractional solutions, we use two various methods such as the sine-cosine and the Jacobi elliptic function methods. The solutions acquired are important in understanding some interesting physical phenomena due to the significance of the Radhakrishnan-Kundu-Lakshmanan equation in designing the propagation of solitons through an optical fiber. Furthermore, we graph some of the obtained solutions in 3D to display the influence of fractional derivative and multiplicative noise on these solutions. Finally, we show that when the order of fractional derivative decreases, the surface shrinks, while the multiplicative noise stabilizes the solutions of FSRKLE a round zero. [ABSTRACT FROM AUTHOR]