Abstarct: Abstract In this thesis, a novel hybrid wavelet-polynomial method is proposed for solving fractional-Volterra optimal control problems with a dimension reduction and enhanced accuracy approach over long time horizons. To this end, two efficient numerical methods baxsed on orthogonal polynomials are introduced: a spectral method using scaled Laguerre polynomials for optimal control problems governed by Volterra integral equations over large intervals, and a Touchard wavelet method for optimal control problems governed by fractional integro-differential equations. In the first method, by employing a suitable exponential transformation, the finite domain [0ⓜ,T] is converted into a semi-infinite domain. Utilizing the orthogonality properties of scaled Laguerre polynomials, the optimal control problem is transformed into a finite-dimensional optimization problem. In the second method, by defining Touchard wavelets and accurately computing their Riemann-Liouville fractional integral operator using hypergeometric functions, the state and control variables are approximated, reducing the problem to a system of algebraic equations. The combination of these two approaches enables solving optimal control problems with high accuracy, dimension reduction, and desirable efficiency over long time intervals. Convergence analysis of the methods is presented, and numerous numerical examples confirm the efficiency and accuracy of the proposed method compared to existing techniques.