Abstract
This paper represents a non-integer-order Vallis systems in which we applied the Grünwald-Letnikov tactics with Binomial coefficients in order to realize the numerical simulations to a set of equations. Recently researchers reported in the literature that it is the generalization of integer order dynamical model. Several cases involving non-integer and integer analysis with different values of non-integer order have been applied to Vallis systems to see the behavior of simulations. To visualize the effect of non-integer order approach, the time histories and phase portraits have been plotted. The consequences expose that the non-integer-order Vallis model can reveal a genuine equitable comportment to Vallis systems and might bid greater perceptions towards the understanding of such complex dynamic systems.
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