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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Fractal Modelling of Dynamical Systems in Association with Weyl-Marchaud Fractional Derivative

Journal of Applied Nonlinear Dynamics 14(2) (2025) 435--461 | DOI:10.5890/JAND.2025.06.013

T.M.C. Priyanka$^1$, A. Gowrisankar$^1$, Bilel Selmi$^2$, Pankajam Natarajan$^3$

$^1$ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India

$^2$ Analysis, Probability & Fractals Laboratory LR18ES17, Department of Mathematics, Faculty of Science of Monastir, University of Monastir, 5000-Monastir, Tunisia

$^3$ Department of Mathematics, School of Engineering and Technology, CMR University, Chagalahatti, Bangalore, 562149, Karnataka, India

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Abstract

The scaling parameters distinguish the fractal interpolation functions from the classical interpolation techniques. While generating hidden variable $A$-fractal function as an attractor for a specific iterated function system, the scaling parameters are considered in the form of upper triangular matrix. As the scalings can be chosen either as constants or functions, in this paper, for both the choices, the Weyl-Marchaud fractional derivative of $A$-fractal function is investigated. The essential conditions are enforced on the upper triangular matrix to demonstrate that the fractional derivative of $A$-fractal function is an attractor for a new iterated function system. To visualize the applications of fractal interpolation functions in the reconstruction process, the Lorenz and R{\"o}ssler attractors of chaotic dynamical systems are reconstructed. Further, the generated fractal attractors consist of more number of data rather than the original chaotic attractors and thus, greatly aids to reveal their hidden self-similar nature.

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