Optimal control of time-fractional convection–diffusion–reaction problem employing compact integrated RBF method

Optimal control has always been investigated for various systems in order to optimize them. It has also been considered as well within convection–diffusion–reaction equations utilizing different methods. The present study introduces a new method for solving the optimal control problem of time-fractional convection–diffusion–reaction using local compact integrated radial basis function (CIRBF). The main idea is to discretize the spatial derivatives by compounding the integrated RBF and compact approach in a stencil. At first, the time-fractional part of the problem is discretized by using the shifted Grünwald formulas. Then, the first- and second-order derivatives of the state and adjoint variables at the nodal points are approximated by the CIRBF method. Moreover, the stability and convergence of the procedure have been proved. Finally, some examples are presented to illustrate the efficiency and accuracy of the process.