STUDY OF PIECEWISE GLOBAL FRACTIONAL FINANCIAL MODEL WITH THREE STATE VARIABLES

Abdul Hameed (), Mati Ur Rahman and Salah Boulaaras
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Abdul Hameed: School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, P. R. China
Mati Ur Rahman: School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, P. R. China3Department of Computer Science and Mathematics, Lebanese American University, Beirut Lebanon
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-16

Abstract: The analysis of nonlinear models and their complex geometrical shapes with globalized piecewise fractional operators for past heredity characteristics serve as the novelty of and motivation for this research. We explore the dynamics of a financial model in the aforementioned framework, using the well known and extensively applied numerical technique of the fractional piecewise Adams–Bashforth method. The effect of the employed parameters on price index, interest rate, investment demand, variation, and expenditure per investment from the saving amount along with the elasticity of the commercial markets demand are investigated. Various fractional orders are simulated in the sense of the Caputo and Atangana–Baleanu Caputo derivatives in the first and second subintervals, respectively. Moreover, the piecewise existence and uniqueness of the solution for the proposed model are established. The concept of Ulam–Hyers stability is applied to the obtained solution. This study will be helpful for beginners to complex geometrical and crossover dynamical problems in various physical and biological sciences.

Keywords: Nonlinear Equations; Fractional Derivatives; Piecewise Global Financial Model; Caputo Operator; ABC Operator; Adams–Bashforth Method; Ulam–Hyers Stability (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400730

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