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A Numerical Scheme Based On Two- And Three-Step Newton Interpolation Polynomials For Fractal–Fractional Variable Orders Chaotic Attractors

Author

Listed:
  • RAJARAMA MOHAN JENA

    (Department of Mathematics, National Institute of Technology Rourkela, Odisha 769008, India)

  • SNEHASHISH CHAKRAVERTY

    (Department of Mathematics, National Institute of Technology Rourkela, Odisha 769008, India)

Abstract

The terms fractional differentiation and fractal differentiation are recently combined to form a new fractional differentiation operator. Several kernels, such as the power-law and the Mittag-Leffler function, are employed to investigate these novel operators. Both fractional-order and fractal dimensions are found in these developed operators. In the present investigation, we have applied these new operators to study certain chaotic attractors with Mittag-Leffler and power-law kernels. These chaotic models are solved using an effective numerical procedure called the Adams–Bashforth technique, based on two- and three-step Newton interpolation polynomials. In this analysis, the order of the fractional derivative is assumed to be the exponential, trigonometric, and hyperbolic forms of variables. The solutions obtained by the numerical procedure with two different kernels are portrayed in terms of chaotic plots.

Suggested Citation

  • Rajarama Mohan Jena & Snehashish Chakraverty, 2022. "A Numerical Scheme Based On Two- And Three-Step Newton Interpolation Polynomials For Fractal–Fractional Variable Orders Chaotic Attractors," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-27, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500931
    DOI: 10.1142/S0218348X22500931
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