A discrete polynomials approach for optimal control of fractional Volterra integro-differential equations

This study develops an efficient numerical method for optimal control problems governed by fractional Volterra integro-differential equations. A new type of polynomials orthogonal with respect to a discrete norm, namely discrete Hahn polynomials, is introduced and its properties investigated. Fractional operational matrices for the orthogonal polynomials are also derived. A direct numerical algorithm supported by the discrete Hahn polynomials and operational matrices is used to approximate solution of optimal control problems governed by fractional Volterra integro-differential equations. Several examples are analyzed and the results compared with those of other methods. The required CPU time assesses the computational cost and complexity of the proposed method.

Automated summary

This study develops an efficient numerical method for solving optimal control problems governed by fractional Volterra integro-differential equations, which has advantages in terms of computational cost and complexity.