Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm

Abstract

The objective of the manuscript is to model and analyze nonlinear waves dynamics through fuzzy-fractional calculus. Since fuzzy logic facilities the waves dynamics to be uncertain, while fractional calculus captures the memory effect inherent in wave propagation. The current study focuses on modeling and analysis of fuzzy-fractional KdV equations namely Burgers KdV, Caudrey-Dodd-Gibbon KdV, and generalized KdV. To include uncertainty in the models, symmetric Gaussian fuzzy numbers are utilized in three different cases at upper and lower bounds in fractional environment. For numerical simulations, hybrid of Mahgoub transformation with homotopy perturbation is proposed and successfully implemented in fuzzy-fractional sense. Validity and competence of proposed methodology is confirmed theoretically by proving existence, uniqueness and convergence. The crest and trough in waves are analyzed in 2D and 3D simulations with respect to time, space, fractional parameter, and k-level sets. The obtained results highlight the accuracy of proposed methodology in case of nonlinear fuzzy-fractional waves dynamics and can be extended to other models in science and engineering.

Keywords

• Fuzzy fractional modeling
• Symmetric Gaussian fuzzy numbers
• KdV Burgers
• Caudrey-Dodd-Gibbon KdV
• Seventh order generalized KdV
• Mahgoub transform