NONLINEAR FRACTIONAL-ORDER FINANCIAL SYSTEM: CHAOTIC BEHAVIOR AND ULAM–HYERS STABILITY

Arunachalam Selvam (), Salah Boulaaras (), Sriramulu Sabarinathan and Taha Radwan
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Arunachalam Selvam: Department of Mathematics & Statistics, School of Applied Sciences and Humanities, Vignan’s Foundation for Science, Technology and Research, Vadlamudi, Guntur 522213, Andhra Pradesh, India
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Sriramulu Sabarinathan: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu 603203, Tamil Nadu, India
Taha Radwan: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-26

Abstract: This study investigates the chaotic behavior and stability of a nonlinear fractional-order financial system utilizing the Caputo fractional derivative. Initially, we formulate the nonlinear fractional-order financial model and establish the problem framework. Next, we prove the existence and uniqueness of solutions by applying the Banach and Schauder fixed-point theorems to the proposed system. Additionally, we analyze the Ulam–Hyers stability and discuss other significant findings related to the system’s stability. To simulate the proposed model, we develop numerical schemes based on fractional calculus, employing Lagrange polynomial interpolation. Finally, we present the numerical simulations to validate the theoretical results, highlighting the significant impact of fractional-order derivatives on the system’s behavior.

Keywords: Chaotic Behavior; Banach- and Schauder-Type Fixed-Point Approaches; Fractional Derivatives; Nonlinear Financial System; Numerical Methods; Ulam–Hyers Stability (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400821

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