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King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems

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  • Soradi-Zeid, Samaneh
  • Jahanshahi, Hadi
  • Yousefpour, Amin
  • Bekiros, Stelios

Abstract

In this study, a new optimization algorithm, called King, is introduced for solving variable order fractional optimal control problems (VO-FOCPs). The variable order fractional derivative is portrayed in the Caputo sense through the dynamics of the system as variable order fractional differential equation (VO-FDE). To this end, firstly, the VO-FOCP is converted into a system of VO-FDEs. Then, according to the fact that the VO-FDE is equivalent to a Volterra integral equation, the system of VO-FDEs is transformed into an equivalent system of variable order fractional integro-differential equations. In the next step, both the context of minimization of total error and a joint application of Banach’s fixed-point theorem are used to solve a nonlinear optimization problem. Actually, using the existing mechanism, the synchronization problem is recast to an optimization problem. Due to the discretization and its board range of arbitrary nodes, the proposed method provides a very adjustable framework for direct trajectory optimization. Finally, the proposed algorithm is verified using several common optimization functions and a chaotic financial system. Also, through simulation results, the proposed method is compared with some popular methods. Simulation results demonstrate the appropriate performance of the introduced method.

Suggested Citation

  • Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305260
    DOI: 10.1016/j.chaos.2019.109569
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    Cited by:

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    7. Wang, Bo & Liu, Jinping & Alassafi, Madini O. & Alsaadi, Fawaz E. & Jahanshahi, Hadi & Bekiros, Stelios, 2022. "Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Wang, Yong-Long & Jahanshahi, Hadi & Bekiros, Stelios & Bezzina, Frank & Chu, Yu-Ming & Aly, Ayman A., 2021. "Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. H. Mesgarani & Y. Esmaeelzade Aghdam & A. Beiranvand & J. F. Gómez-Aguilar, 2024. "A Novel Approach to Fuzzy Based Efficiency Assessment of a Financial System," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1609-1626, April.
    10. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    12. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    13. Malik, Muhammad Faizan & Chang, Ching-Lung & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa kausar & Shu, Chi-Min & Raja, Muhammad Asif Zahoor, 2023. "Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    14. Alsaadi, Fawaz E. & Bekiros, Stelios & Yao, Qijia & Liu, Jinping & Jahanshahi, Hadi, 2023. "Achieving resilient chaos suppression and synchronization of fractional-order supply chains with fault-tolerant control," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    15. Zhou, Shuang-Shuang & Jahanshahi, Hadi & Din, Qamar & Bekiros, Stelios & Alcaraz, Raúl & Alassafi, Madini O. & Alsaadi, Fawaz E. & Chu, Yu-Ming, 2021. "Discrete-time macroeconomic system: Bifurcation analysis and synchronization using fuzzy-based activation feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    16. Chen, Shu-Bo & Jahanshahi, Hadi & Alhadji Abba, Oumate & Solís-Pérez, J.E. & Bekiros, Stelios & Gómez-Aguilar, J.F. & Yousefpour, Amin & Chu, Yu-Ming, 2020. "The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    17. Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    18. Wang, Shaojie & Bekiros, Stelios & Yousefpour, Amin & He, Shaobo & Castillo, Oscar & Jahanshahi, Hadi, 2020. "Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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