The shifted Jacobi polynomial integral operational matrix for solving Riccati differential equation of fractional order

In this article, we have applied Jacobi polynomial to solve Riccati differential equation of fractional order. To do so, we have presented a general formula for the Jacobi operational matrix of fractional integral operator. Using the Tau method, the solution of this problem reduces to the solution of a system of algebraic equations. The numerical results for the examples presented in this paper demonstrate the efficiency of the present method

Appell Type Changhee Polynomials Operational Matrix of Fractional Derivatives and its Applications

In this paper, a fractional order differential equation (FDEs), will be solved numerically through a new approximative technique based on Appell type Changhee polynomials. The operational of fractional order derivative will be constructed, then its application together with collocation method in solving fractional differential equations (FDEs) will be presented. The fractional derivatives in the FDEs are described in the Caputo sense. Some numerical examples are finally given to show the accuracy and applicability of the new operational matrix