ADAMS–BASHFORTH NUMERICAL METHOD-BASED SOLUTION OF FRACTIONAL ORDER FINANCIAL CHAOTIC MODEL

Rajarama Mohan Jena, Snehashish Chakraverty (), Shengda Zeng () and Nguyen van Thien ()
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Rajarama Mohan Jena: Department of Mathematics, C. V. Raman Global University, Bhubaneswar 752054, India
Snehashish Chakraverty: Department of Mathematics, National Institute of Technology, Rourkela 769008, India
Shengda Zeng: Yulin Normal University, Yulin 537000, Guangxi, P. R. China
Nguyen van Thien: Department of Mathematics, FPT University, Education zone, Hoa Lac High Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam

FRACTALS (fractals), 2023, vol. 31, issue 07, 1-15

Abstract: A new definition of fractional differentiation of nonlocal and non-singular kernels has recently been developed to overcome the shortcomings of the traditional Riemann–Liouville and Caputo fractional derivatives. In this study, the dynamic behaviors of the fractional financial chaotic model have been investigated. Singular and non-singular kernel fractional derivatives are used to examine the proposed model. To solve the financial chaotic model with nonlocal operators, the fractional Adams–Bashforth method (ABM) is applied based on Lagrange polynomial interpolation (LPI). The existence and uniqueness of the solution of the model can be demonstrated using fixed point theory and nonlinear analysis. Further, the error analysis of the present method and Ulam–Hyers stability of the considered model have also been included. Obtained numerical simulations reveal that the model based on three different fractional derivatives shows various chaotic behaviors that may be useful in a practical sense which may not be observed in the integer case.

Keywords: Fractional Calculus; Lagrange Interpolation; Power-Law Kernel; Mittag-Leffler Kernel; Financial Chaotic Model; Exponential Decay Kernel (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500871

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