Analysis of 3D IS-LM macroeconomic system model within the scope of fractional calculus

被引：18
作者：
Bonyah E. [1 ]
Atangana A. [2 ]
Chand M. [3 ]
机构：
[1] Department of Mathematics Education, University of Education Winneba(Kumasi campus), Kumasi
[2] Institute for Groundwater Studies, University of the Free State, Bloemfontein
[3] Department of Mathematics, Baba Farid College, Bathinda
来源：
Chaos, Solitons and Fractals: X | 2019年 / 2卷
关键词：
Macro-economic system; New adams-Bashforth for fractional differential equations; Singular and non-singular kernels; Stochastic model;
D O I：
10.1016/j.csfx.2019.100007
中图分类号：
学科分类号：
摘要：
A mathematical model providing an asymptotic description of macro-economic system is considered in this work. The system in general deals with performance, behaviour, decision-making of an economy as a whole and also the structure. Due to the complexities of this system, a more complex mathematical model is requested. In this work, we considered the extension of the model using some non-local differential operators and the stochastic approach where the given parameters are converted to normal distributions. We have presented the conditions of existence of uniquely exact solutions of the system using the fixed-point theorem approach. Each model is solved numerical via a newly introduced modified Adams-Bashforth for fractional differential equations. We presented numerical simulations for different values of fractional order. The models with the Atangana-Baleanu and Caputo differential operators provided us with new attractors. © 2019
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  • [1] Oldham K.B., Spanier J., The fractional calculus, (1999)
  • [2] Podlubny I., Fractional differential equations, (1999)
  • [3] Miller K.S., Ross B., An introduction to the fractional calculus and fractional differential equations, (2003)
  • [4] Caputo M., Linear models of dissipation whose q is almost frequency independent: part ii, J Roy Astronom Soc, 13, pp. 529-539, (1967)
  • [5] Khan Y., Faraz N., Kumar S., Yildirim A., Coupling method of homotopy perturbation and laplace transformation for fractional models, UPB Sci Bull, Series A, 741, (2012)
  • [6] Atangana A., Goufo E.F.D., Computational analysis of the model describing hiv infection of CD4<sup>+</sup>T cells, Biomed Res Int, 2014, (2014)
  • [7] He J., Approximate analytical solution for seepage flow with fractional derivative in porous media, Comput Methd Appl Mech Eng, 167, pp. 57-68, (1998)
  • [8] Farai N., Khan Y., Sankar D.S., Decomposition-transform method for fractional differential equations, Internat J Nonlinear Sci Numer Simulation, 11, pp. 305-310, (2010)
  • [9] Khan Y., Farai N., Yildirim A., Wu Q., Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science, Comput Math Appl, 62, pp. 2273-2278, (2011)
  • [10] Odibat Z., Momani S., Application of variational iteration method to nonlinear differential equations of fractional order, Int J Nonlinear Sci Numer Simulation, 7, pp. 27-34, (2006)
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