TY - JOUR
TI - Exploring multiple and singular soliton solutions for negative-order space-time fractional mKdV equations
AU - Zubair Sulima
AU - Ahmed Hala
AU - Mahmoud Batul
AU - Elamin Safa
AU - Atti Hind
AU - Younis Bakri
JN - Thermal Science
PY - 2025
VL - 29
IS - 1
SP - 359
EP - 370
PT - Article
AB - This study on the negative-order fractional space-time modified KdV (nfmKdV)  equation provides a comprehensive analysis of how fractional differentials  affect the dynamics of solitons in non-linear wave models. We are referring  to introduces the nfmKdV equation, a significant extension of the  traditional KdV equation, which is commonly used to model wave propagation  in non-linear dispersive media. By developing both focusing and defocusing  solutions and employing the Hirota technique to construct multisoliton  solutions, the study opens new avenues for the exploration of fractional  wave equations in diverse physical contexts. The use of fractional  calculus, and specifically negative-order derivatives, enhances the model's  ability to describe real-world phenomena with long-range interactions and  memory effects, offering significant potential for future research in  non-linear and fractional dynamics. This newly established result warrants  further investigation determine its applicability to other non-linear  fractional order models, and other existing methods may be employed to  explore this new development. As the fractional order approaches one, the  results align with well-established findings in the literature. This study  provides a deeper understanding of the dynamics of solitons in fractional  media, which could be useful for modelling soliton propagation in systems  where traditional integer-order models fail to capture essential behavior.