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This paper presents an efficient numerical technique for solvingmulti-dimensional fractional optimal control problems using fractional-ordergeneralized Bernoulli wavelets. The numerical results obtained by this methodhave been compared with the results obtained by the method using orthonormalBernoulli wavelets. Using fractional-order generalized Bernoulli wavelets,product and integral operational matrices have been obtained. By using theseoperational matrices, the multi-dimensional fractional optimal control problemshave been reduced into a system of algebraic equations. To confirm theefficiency of the proposed numerical technique involving fractional-ordergeneralized Bernoulli wavelets, numerical problems have been solved by usingboth orthonormal Bernoulli wavelets and fractional-order generalized Bernoulliwavelets and obtaining an approximate cost function value, which has been foundby approximating state and control functions. In addition, the convergence rateand error bound of the proposed numerical method have also been derived.

Comparison of fractional-order generalized wavelets and orthonormal  wavelets methods for solving multi-dimensional fractional optimal control  problems