Abaker A. Hassaballa1,2, Ali Satty2This email address is being protected from spambots. You need JavaScript enabled to view it., Mohyaldein Salih2, Ahmed M. A. Adam2, Omer M. A. Hamed3, Zakariya M. S. Mohammed1,2, Ashraf F. A. Mahmoud4,5, and Elzain A. E. Gumma2
1Center for Scientific Research and Entrepreneurship, Northern Border University, Arar, Saudi Arabia
2Department of Mathematics, College of Science, Northern Border University, Arar, Saud Arabia
3Department of Finance, College of Business Administration, Northern Border University, Arar, Saudi Arabia
4Translation, Authorship and Publication Center, Northern Border University, Arar, Saudi Arabia
5Department of Computer Science, College of Science, Northern Border University, Arar, Saudi Arabia
Received: January 6, 2025 Accepted: May 12, 2025 Publication Date: June 15, 2025
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
The article examines the fractional stochastic Korteweg-de Vries (FSKdV) equation, with a focus on space-time white noise and conformable fractional derivatives (CFD). The primary aim is to utilize the generalized Riccati equation mapping (GREM) method to derive soliton and soliton-like, periodic and rational solutions for the FSKdV equation, taking into account various conditions of space-time fractional order beside white noise as well. The acquired exact analytical solutions’ physical characteristics are elucidated through graphical illustrations, which clearly show the effects of changing the fractional order and including the stochastic term. The results confirm the GREM method’s reliability and effectiveness in solving the FSKdV equation.
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