# Numerical Techniques for Fractional Competition Dynamics with Power-, Exponential- and Mittag-Leffler Laws

• Hemen Dutta
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)

## 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 $$\alpha$$. In the simulation framework, we consider a number of fractional competition dynamics arising in applied areas of engineering and science.

## Keywords

Atangana-Baleanu derivative Fractional Adams-Bashforth-Moulton methods Fractional order competition dynamics Numerical simulations Stability analysis

## 2010 Mathematics Subject Classification:

34A34 35A05 35K57 65L05 65M06 93C10

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