Fractional hyper-chaotic model with no equilibrium

This paper considers a novel four dimensional dynamical model containing hyper-chaotic attractors. The concept fractional differential based on the exponential and Mittage-Leffler kernel were used to extend the classical version in order to include into the mathematical formulation the crossover in waiting time distribution. We have presented for both models the conditions under which the existence and the uniqueness of exact solutions are reached.We have used a newly established numerical scheme, that combines the fundamental theorem of fractional calculus and the Lagrange interpolation polynomial to solve the system numerically. We presented some numerical simulations for different values of fractional order, we compared both models with the existing one under the framework of fractional calculus. Our model has shown very new chaotic features in particular with the Atangana-Baleanu fractional derivative.