Shifted Genocchi Polynomials Operational Matrix for Solving Fractional Order System

Genocchi polynomials are known to be defined on the interval [0, 1], but to benefit from the advantages of this polynomials in the field of fractional differential equations (FDEs), it was realized that fractional derivatives of many functions with arbitrary order cannot always be defined at x = 0. To avoid this difficulty, the idea of shifting from the interval [0, 1] to the interval [1, 2] makes it simple and applicable. Interestingly, almost all the properties of the Genocchi polynomials are inherited by the shifted polynomial. Therefore, in this research we construct shifted Genocchi polynomial’s operational matrix of arbitrary order derivative and used it with the collocation method to solve some systems of FDEs.