Non standard finite difference method for solving variable order fractional optimal control problems

A modified numerical technique was developed to solve a wide class of variable order fractional optimal control problems in the sense of Riemann Liouville or Caputo derivatives. The modified algorithm is based on the non-standard finite difference method of solving fractional differential equations of variable order. Important property of a reflection operator is used to simplify the variable order right Riemann Liouville or Caputo derivatives to the variable order left Riemann Liouville or Caputo derivatives. Necessary and sufficient conditions that guarantee the existence and the uniqueness of the solution of the resulting systems are given. Illustrative examples are included to demonstrate the validity and the effectiveness of the established approach.