Research Article The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method Farah M. Al-Askar 1 and Wael W. Mohammed 2,3 1 Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia 2 Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia 3 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt Correspondence should be addressed to Wael W. Mohammed; wael.mohammed@mans.edu.eg Received 21 June 2022; Revised 13 July 2022; Accepted 30 July 2022; Published 15 August 2022 Academic Editor: Qura tul Ain Copyright © 2022 Farah M. Al-Askar and Wael W. Mohammed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero. 1. Introduction Deterministic partial differential equations (DPDEs) are uti- lized to explain the dynamic behavior of the phenomena in physics and other scientific areas including nonlinear optics, biology, elastic media, fluid dynamics, molecular biology, hydrodynamics, surface of water waves, quantum mechanics, and plasma physics. As a result, solving nonlinear problems is crucial in nonlinear sciences. Some of these methods, such as Darboux transformation [1], sine-cosine [2, 3], exp ð−ϕðς ÞÞ-expansion [4], ðG′ /GÞ-expansion [5, 6], Hirota’s function [7], perturbation [8, 9], Jacobi elliptic function [10, 11], trial function [12], tanh-sech [13], fractal semi-inverse method [14, 15], F-expansion method [16], and homotopy perturba- tion method [17], have been recently developed. However, it is completely obvious that the phenomena that happen in the environment are not always deterministic. Recently, fluc- tuations/noise has been demonstrated to play an important role in a wide range in describing different phenomena that appear in oceanography, environmental sciences, finance, meteorology, information systems, biology, physics, and other fields [18–24]. Therefore, partial differential equations with noise or random effects are ideal mathematical problems for modeling complex systems. On the other hand, fractional partial differential equa- tions (FPDEs) have been used to explain many physical phenomena in biology, physics, finance, engineering appli- cations, electromagnetic theory, mathematical, signal pro- cessing, and different scientific studies; see, for example, [25–35]. These new fractional-order models are better equipped than the previously utilized integer-order models because fractional-order integrals and derivatives allow for the representation of memory and hereditary qualities of dif- ferent substances [36]. Compared to integer-order models, where such effects are ignored, fractional-order models have the most significant advantage. Hindawi Advances in Mathematical Physics Volume 2022, Article ID 1534067, 8 pages https://doi.org/10.1155/2022/1534067