Orthonormal shifted discrete Hahn polynomials for a new category of nonlinear variable-order fractional 2D optimal control problems

The present work provides a formulation for the orthonormal shifted discrete Hahn polynomials on an arbitrary domain. We also extract some useful matrix relationshipsrelating to these discrete polynomials. These polynomials and the obtained relations are employed with the Lagrange multipliers technique to design a numerical method for solving a class of variable-order (VO) fractional 2D optimization problems subject to Robin boundary value conditions. The proposed method converts the VO fractional system into a system of algebraic equations which readily can be solved. Some numerical examples are studied to validate and illustrate the accuracy of the introduced technique.