A computational method based on the generalized Lucas polynomials for fractional optimal control problems

Abstract Nonorthogonal polynomials have many useful properties like being used as a basis for spectral methods, generated in an easy way, having exponential rates of convergence, fewer terms and reducing computational errors comparison with some others, producing most important basic polynomials. In this regard, paper deals new indirect numerical method to solve fractional optimal control problems based on the generalized Lucas Through left right Caputo derivatives operational matrices these are derived. Based Pontryagin maximum principle, necessary optimality conditions problem reduce into two-point boundary value problem. The main efficient characteristic behind proposed is convert under consideration system algebraic equations which reduces costs CPU time. To demonstrate efficiency, applicability, simplicity method, several examples solved, obtained results compared those other methods.