In this paper, we introduce a method to solve systems of linear Fredholm integro-differential equations in terms of Fibonacci polynomials. First, we present some properties of these polynomials then a new approach implementing a collocation method in combination with matrices of Fibonacci polynomials is introduced to approximate the solution of high-order linear Fredholm integro-differentail equations systems with variable coefficients under the mixed conditions. Numerical results with comparisons are given to confirm the reliability of the proposed method for solving these systems of equations.
