Numerical techniques for fractional competition dynamics with power-, exponential- and mittag-leffler laws

Abstract

This chapter deals with modelling and analysis fractional competition system with power law, exponential law and the Mittag-leffler law in which the standard derivative in time is replaced with the Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. A fractional version of the Adams-Bashforth scheme is formulated for the approximation of these derivatives. To justify the applicability and suitability of these derivatives, we drawn comparison by applying them to solve some problems for specific value of fractional power α. In the simulation framework, we consider a number of fractional competition dynamics arising in applied areas of engineering and science.