A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left- and right-sided derivatives. The main ingredient the proposed method is recast problem into an equivalent system weakly singular integral equations. Then, Legendre-based spectral collocation developed for solving transformed system. Therefore, we can make good use advantages Gauss quadrature rule. present construction analysis method. These results be indirectly applied optimal control by considering corresponding Euler–Lagrange Two numerical examples are given confirm convergence robustness scheme.