A novel Legendre operational matrix for distributed order fractional differential equations

摘要

In this paper, for the first time, the shifted Legendre operational matrix of distributed order fractional derivative has been derived. Also, this new operational matrix is used together with tau method for approximation of solutions of linear distributed order fractional differential equations and diffusion equations with distributed order in time. Moreover, eight numerical examples are implemented in order to show the validity and reliability of the suggested methods.