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.
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