Solvability of chaotic fractional systems with 3D four-scroll attractors

One of the questions that has recently predominated the literature is the generation and modulation of strange chaotic attractors, namely the ones with multi scrolls. The fractional theory might be useful in addressing the questions. We use the Caputo fractional derivative together with Haar wavelet numerical scheme to investigate a three-dimensional system that generates chaotic four-wing attractors. Some conditions of stability at the origin (the trivial equilibrium point) are provided for the model. The error analysis shows that the method converges and is concluded thanks to Fubini-Tonelli theorem for non-negative functions and the Mean value theorem for definite integrals. Graphical simulations, performed for some different value of the derivative order α show existence, as expected, of chaotic dynamics characterized by orbits with four scrolls, typical to strange attractors. Hence, fractional calculus appears to be useful in generating and modulating chaotic multi-wing attractors.