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

Nasser H. Sweilam, Muner M. Abou Hasan and Dumitru Baleanu

Chaos, Solitons & Fractals, 2017, vol. 104, issue C, 772-784

Abstract: 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.

Keywords: Financial models for awareness and trial; Nonstandard finite difference method; Jacobi polynomials; Collocation method; Fractional derivative (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:104:y:2017:i:c:p:772-784

DOI: 10.1016/j.chaos.2017.09.013

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