A New Solution for Optimal Control of Fractional Convection–Reaction–Diffusion Equation Using Rational Barycentric Interpolation


This paper solves an optimal control problem governed by a fractional convection–reaction–diffusion partial differential equation. Using Lagrangian multipliers, necessary conditions are obtained, and then, Barycentric collocation method are applied for discretizing classical derivatives and Grünwald–Letnikov formula for fractional derivative. Barycentric interpolation is a class of Lagrange polynomial interpolation that is fast and deserves to be known as a method of polynomial interpolation and Grünwald–Letnikov formula is a basic extension of the derivative in fractional calculus. Numerical examples are presented to show the effectiveness of the method.

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Correspondence to Majid Darehmiraki.

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Darehmiraki, M., Rezazadeh, A. A New Solution for Optimal Control of Fractional Convection–Reaction–Diffusion Equation Using Rational Barycentric Interpolation. Bull. Iran. Math. Soc. 46, 1307–1340 (2020). https://doi.org/10.1007/s41980-019-00327-y

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  • Optimal control
  • Partial differential equation
  • Convection–reaction fractional equation
  • Grünwald–Letnikov formula
  • Barycentric collocation method

Mathematics Subject Classification

  • 43A62
  • 42C15