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• A comparative performance of Chebyshev spectral methods coupled with domain decomposition in solving hyperchaotic finance systems of differential equations is offered. • The proposed methods are fast, robust and offer exponential convergence. • A preference is given to spectral integral approach. It is elegant and accurate. A comparative performance analysis of two spectral methods on the hyperchaotic finance system (HCFS) and the cryptocurrency pricing problem (CPP) is proposed. The first approach uses a differentiation matrix, the second method considers an integration matrix on a single and multiple domains when the time intervals are large. Numerical simulations are performed against the well established numerical method, Chebfun. It turns out that the spectral method using itegration matrix is more efficient than the other methods on both problems. [ABSTRACT FROM AUTHOR]

• Chaotic systems such as: the fractal-fractional hyperchaotic finance system and the fractal-fractional Bloch system with time delay are studied. • Two Grüijnwald-Letnikov nonstandard finite difference schemes are presented to study the proposed chaotic systems. • The stability analysis of the used methods are proved. • Comparative studies. The purpose of this paper is to study numerically the behavior of two novel different classes of fractional order chaotic systems. These systems are; the fractal-fractional hyperchaotic finance system and the fractal-fractional Bloch system with time delay. The fractal-fractional derivatives are defined in the Caputo and Riemann-Liouville senses. Two Grünwald-Letnikov nonstandard finite difference schemes are presented to study the proposed chaotic systems. Moreover the stability analysis of the used methods are proved. In order to show the simplicity and effectively of the proposed methods, numerical simulations and comparative studies are given. [ABSTRACT FROM AUTHOR]