Abstract
Chaotic dynamical systems are studied in this paper. In the models, integer order time derivatives are replaced with the Caputo fractional order counterparts. A Chebyshev spectral method is presented for the numerical approximation. In each of the systems considered, linear stability analysis is established. A range of chaotic behaviours are obtained at the instances of fractional power which show the evolution of the species in time and space.
Highlights
Fractional differential systems are largely encountered in various fields of applied sciences and engineering [1,2,3,4,5]
We briefly report the behaviour of fractional order chaotic systems (8) and
We provide an extension to system (11) to form a Caputo fractional reaction-diffusion problem as: C
Summary
Fractional differential systems are largely encountered in various fields of applied sciences and engineering [1,2,3,4,5]. The study of differential equations of noninteger-order derivative have made tremendous development in terms of theory and application. It encompasses the general extension of classical order integrals and derivatives to fractional order counterparts. The main advantage of such models is the introduction of a fractional parameter, say γ which can be used to model non-Markovian behaviour of spatial or temporal processes. This technique has emerged over the years as generalisations of many classic scenarios in mathematical physics
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