Exact soliton solutions to the Cahn–Allen equation and Predator–Prey model with truncated M-fractional derivative

Abstract

The current research is about new exact soliton solutions to the Cahn–Allen equation and Predator–Prey model with the most general fractional derivative operator. The novel truncated M-fractional derivative is applied to study the aforementioned models to secure soliton solutions via the modified integration scheme known as the extended Sinh–Gordon equation expansion method (ShGEEM). This study provides the dark, singular, singular-dark, kink solitons and other solutions with certain conditions. The gained results are also verified with the use of symbolic software. The obtained solutions may be applied in the demonstration of the Cahn–Allen equation and Predator–Prey model in some better way using a fractional derivative. These solutions suggest that this method is more effective, straight forward and reliable as compared to other methods.