Fractional order modeling and simulation of a multi-bond orbital chaotic system via Caputo-Fabrizio operators

Elekanyani Madia; Anastacia Dlamini; Emile Franc D. Goufo; Melusi Khumalo; Elekanyani Madia; Anastacia Dlamini; Emile Franc D. Goufo; Melusi Khumalo

doi:10.3934/math.20251125

AIMS Mathematics

2025, Volume 10, Issue 11: 25406-25433. doi: 10.3934/math.20251125

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Fractional order modeling and simulation of a multi-bond orbital chaotic system via Caputo-Fabrizio operators

Department of Mathematical Sciences, University of South Africa, Florida Campus, 0003, South Africa

Received: 18 May 2025 Revised: 30 July 2025 Accepted: 06 August 2025 Published: 05 November 2025
MSC : 26A33, 34A08, 34D45, 37D45, 65P20

Chaotic systems play a crucial role in science and engineering due to their complex and unpredictable behavior. In this study, we investigated a nonlinear chaotic system known as the multi-bond orbital chaotic attractor (MBOCA), which we modeled using the Caputo Fabrizio fractional operators. We first established the existence and uniqueness of solutions for the system after applying these operators to the MBOCA. We then presented a numerical scheme and analyzed its stability and convergence. To validate the proposed numerical scheme, we performed numerical simulations to visualize the system's behavior for both integer and fractional order cases. The results confirmed that the generated bond-orbital attractors exhibit chaotic behavior, highlighting the influence of fractional order operators on the system's dynamic complexity.
Citation: Elekanyani Madia, Anastacia Dlamini, Emile Franc D. Goufo, Melusi Khumalo. Fractional order modeling and simulation of a multi-bond orbital chaotic system via Caputo-Fabrizio operators[J]. AIMS Mathematics, 2025, 10(11): 25406-25433. doi: 10.3934/math.20251125

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Abstract

Chaotic systems play a crucial role in science and engineering due to their complex and unpredictable behavior. In this study, we investigated a nonlinear chaotic system known as the multi-bond orbital chaotic attractor (MBOCA), which we modeled using the Caputo Fabrizio fractional operators. We first established the existence and uniqueness of solutions for the system after applying these operators to the MBOCA. We then presented a numerical scheme and analyzed its stability and convergence. To validate the proposed numerical scheme, we performed numerical simulations to visualize the system's behavior for both integer and fractional order cases. The results confirmed that the generated bond-orbital attractors exhibit chaotic behavior, highlighting the influence of fractional order operators on the system's dynamic complexity.

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