The authors present a robust numerical scheme for solving linear and non-linear mixed-order fractional differential equations. In the proposed technique, a matrix is designed to solve fractional order derivatives for shifted Jacobi polynomials. The key feature of this strategy is that the problems are reduced to a set of algebraic equations by using the shifted Jacobi spectral method for linear and non-linear multi-term fractional differential equations. An exact solution for proposed equations, when functions are polynomials, is presented. Numerous tested problems demonstrate the effectiveness and applicability of the suggested method.