In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.

This work presents alternative solutions of the fractional waves in dielectric media using the Atangana–Baleanu fractional operator in Liouville-Caputo and Riemann–Liouville sense, the order considered is for the space-time domain. We solved analytically the fractional equation using the properties of Laplace transform operator together with the convolution theorem. New results are presented and the analytical solutions are given in terms of the multivariate Mittag-Leffler functions preserving the physical units of the system studied. Numerical simulations were performed for different values of fractional order.