Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems

Abstract In this work, a technique for finding approximate solutions ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is hybrid between Galerkin and collocation methods. Also, can be extended to fractional integro-differential (FIDEs) optimal control problems (FOCPs). spatial approximations with their derivatives are based on shifted ultraspherical polynomials (SUPs). Modified spectral used create direct linear/nonlinear equations, system or problems. aim transform those into algebraic equations. That will efficiently solved by solver. Three spaces nodes have through that transformation. Finally, numerical examples show the accuracy efficiency investigated method.