AN IMPROVED COLLOCATION TECHNIQUE FOR DISTRIBUTED-ORDER FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

This paper addresses spectral collocation techniques to treat with the distributed-order fractional partial differential equation (DOFPDE). We introduce a new shifted fractional order Jacobi orthogonal function (SFOJOF) outputted by Jacobi polynomials. Also, we state some corollaries and theorems related to new SFOJOF. The shifted Jacobi-Gauss-Lobatto collocation (SJ-GL-C) and shifted fractional order Jacobi-Gauss-Radau collocation (SFJ-GR-C) methods are developed for approximating the DOFPDEs. The basis of the shifted Jacobi polynomial is adapted for spatial discretization and another basis of SFOJOF is investigated for temporal discretization. Through the selected basis functions, the related conditions are automatically accomplished. The principal target in our technique is to transform the DOFPDE to a system of algebraic equations. Some numerical examples are given to test the accuracy and applicability of our technique.