Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system

M. H. Heydari*, M. Razzaghi, Z. Avazzadeh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In this paper, a novel fractal-fractional derivative operator with Mittag-Leffler function as its kernel is introduced. Using this differentiation, the fractal-fractional model of the coupled nonlinear Schrödinger-Boussinesq system is defined. The orthonormal shifted discrete Chebyshev polynomials are generated and used for constructing a computational matrix method to solve the defined system. In the established method, using the matrices of the ordinary and fractal-fractional differentiations of these polynomials, the fractal-fractional system transformed into a system of algebraic equations, which is solved readily. Practicability and precision of the method are examined by solving two numerical examples.

Original languageEnglish
Article number110570
JournalChaos, Solitons and Fractals
Publication statusPublished - Feb 2021


  • Coupled nonlinear FF Schrödinger-Boussinesq equations
  • Fractal-fractional (FF) derivative
  • Orthonormal shifted discrete Chebyshev polynomials

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