Abstract:
This work considers a new generalized operator which is based on the application of Caputo-type fractional
derivative is applied to model a number of nonlinear chaotic phenomena, such as the Oiseau mythique
Bicéphale, Oiseau mythique and L’Oiseau du paradis maps. Numerical approximation of the generalized
Caputo-type fractional derivative using the novel predictor–corrector scheme, which indeed is regarded as
an extension of a well-known Adams–Bashforth–Moulton classical-order algorithm. A range of new strange
chaotic wave propagation was observed for various maps with varying fractional parameters.
