New studies for general fractional financial models of awareness and trial advertising decisions

• Published in: Chaos, solitons and fractals solitons and fractals, 2017-11, Vol.104, p.772-784
• Main Authors: Sweilam, Nasser H., Abou Hasan, Muner M., Baleanu, Dumitru
• Format: Article
• Language: English
• Subjects: Collocation method; Financial models for awareness and trial; Fractional derivative; Jacobi polynomials; Nonstandard finite difference method
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2017.09.013

•Financial models for awareness and trial.•The nonstandard finite difference method.•The Jacobi–Gauss–Lobatto spectral collocation method (collocation method.•Positivity and boundedness of a scheme. In this paper, two numerical techniques are introduced to study numerically the general fractional advertising model. This system describes the flux of the consumers from unaware individuals group to aware or purchased group. The first technique is an asymptotically stable difference scheme, which was structured depending on the nonstandard finite difference method. This scheme preserves the properties of the solutions of the model problem as the positivity and the boundedness. The second technique is the Jacobi–Gauss–Lobatto spectral collocation method which is exponentially accurate. By means of this approach, such problem is reduced to solve a system of nonlinear algebraic equations and are greatly simplified the problem. Numerical comparisons to test the behavior of the used techniques are run out. We conclude from the computational work that: the Jacobi–Gauss–Lobatto spectral collocation method is more accurate whereas the nonstandard finite difference method requires less computational time.