Sensitivity analytic and synchronization of a new fractional-order financial system

Document Type : Research Paper


Department of mathematics, Payame Noor, Tehran, Iran.


In this paper, we present a new fractional-order financial system (FOFS) with the new parameters. We study the synchronization for commensurate order of the fractional-order financial system with disturbance observer (FOFSDO) on the new parameters. Also, the sensitivity analysis of the synchronization error was investigated by using the feedback control technique for the FOFSDO. The stability of the used method demonstrates by Lyapunov stability theorem. Numerical simulations are presented to ensure the validity and influence of the target feedback control design in the presence of extrinsic bounded unknown disturbance.


[1] N. Aguila-Camacho, M. A. Duarte-Mermoud, and J. A. Javier Gallegos, Lyapunov functions for fractional order system, Common Nonlinear sci. Numer. sim., 19 (2014), 2951–2957.
[2] B. Bandyopadhyay and S. Kamal, Stabilization and control of fractional-order systems: A sliding mode Approach, springer, 2015.
[3] L. Changpin and D. Weihua, Remarks on fractional derivatives, App. Math. Comput., 187 (2007), 777–784.
[4] G. Chen and X. Dong, From chaos to order methodologies, perspectives, and applications, Word Scientific, Singapore, 1998.
[5] W. C. Chen, Nonlinear dynamics and chaos in a fractional-order financial system, Chaos Solitons Fractal, 36 (2006), 1305–1314.
[6] A. L. Chian, E. L. Rempel, and C. Rogers, Complex economic dynamics: Chaotic saddle, crisis, and intermittency, Chaos Solitons Fractals, 29 (2006), 1194–1218.
[7] A. L. Chian, F. A. Zorotta, E. L. Rempel, and C. Rogers, Attractor emerging crisis in chaotic business cycles, Chaos Solitons Fractal, 24, (2005), 869–875.
[8] S. Dadras and H. R. Momeni, Control of a fractional-order economical system via sliding mode, Physical A, 389 (2010), 2434–2442.
[9] M. F. Danca, R. Garrappa, W. K. S Tang, and G. Chen, Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching, computers and mathematics with Applications, 66 (2013), 702–716.
[10] A. Hajipour and H. Tavakoli, Analysis and circuit simulation of a novel nonlinear fractional incommensurate order financial system, Optik 127(22) ()2016, 10643–10652.
[11] A. Khan and A. Tyagi, Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems, Pramana J. Phys., 90(67) (2018), DOI:10.1007/s12043-018-1555-8.
[12] J. H. Ma and Y. S. Chen, Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system(I), Appl. Math., 22(11) (2001), 1119–1128.
[13] J. H. Ma and Y. S. Chen,Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system(II), Appl. Math., 22(12) (2001), 1236–1242.
[14] D. Matignon, Stability results for fractional differential equations with applications to control processing, Computational Engineering in Systems Applications, 2 (1996), 963–968.
[15] R. A. Meyers, Complex system in Finance and Econometrics, Springer, New York, 2009.
[16] B Naderi, H. Kheiri, and V. Vafaei, Modified Sliding-Mode Control Method for Synchronization a Class of Chaotic Fractional-Order Systems with Application in Encryption, The ISC International Journal of Information Security, 12(1) (2020), 55–66.
[17] I. Petras, Fractional-order nonlinear systems, modeling, analysis, and simulation, Higher Education Press and Springer, Beijing, 2011.
[18] C. K. Tacha, I. M. Volos, I. N. Kyaprianidis, S. Stouboulos, and V. T. P. Vaidyanathan, Analysis, adaptive control and circuit simulation of a novel nonlinear finance systemm, App. Math. Comput., 276 (2016), 200–217.
[19] O. I. Tacha, J. M-Munoz-Pacheco, E. Zambrano-Serrano, I. N. Stouboulos, and T. Pham-V Determining the chaotic behavior in a fractional-order finance system with negative parameters, Nonlinear Dyn., (2018), DOI:10.1007/s11071-018-4425-5.
[20] Z. Wang and X. Huang, Synchronization of a chaotic fractional-order economical system with active control, Procida Engineering, 15 (2010), 516–520,
[21] B. Xin, and J. Zhang, Finite-time stabilizing a fractional-order chaotic financial system with market confidence, Nonlinear Dyn., 79(2) (2015), 1399–1409.