Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem.

This work presents an effective numerical approach to solving variable-order multi-dimensional fractional optimal control problems. Utilizing well-known formulas such as the variable-order Caputo derivative and variable-order Riemann–Liouville integral, we determine the variable-order operational matrices and product operational matrices for the fractional Chelyshkov wavelet. By using the operational matrices, the process of solving the variable-order multi-dimensional fractional optimal control problem is simplified to a system of algebraic equations. Finally, using the Lagrange multiplier technique, we obtain the approximate cost function based on determining the state and control functions. We establish the convergence analysis and error bounds for the proposed method. To check the veracity of the presented method, we solve some numerical examples. [ABSTRACT FROM AUTHOR]