The present study focuses on a class of Korteweg-de Vries (KdV)-type equations involving the time-space fractal scaling law derivative. The objective of this investigation is to explore their exact analytical solutions. The employment of fractal scaling law derivatives, calculus theory, and Jacobi elliptic functions, in conjunction with variable substitutions and equation transformations, facilitates the attainment of precise analytical solutions for this equation type under various conditions. The findings of the research endeavor have yielded two notable outcomes. Firstly, they have augmented the solution system for KdV-type equations. Secondly, they have furnished an effective method reference for solving other non-linear fractal partial differential equations. These contributions are instrumental in fostering the advancement of the application of fractal calculus in the domain of mathematical physics.
Wenze Dong (Thu,) studied this question.
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