Weighted residual strategy to solve distributed-order fractional differential equations

A novel method to finding the numerical solution of distributed-order fractional differential equations (DFDEs) is introduced. This method is based on Genocchi wavelets (GWs), and weighted residual method (collocations method). For this aim, an exact formula involving regularized beta functions for determining the Riemann-Liouville fractional integral operator of these wavelets is given. Implementing the mentioned integral operator with the help of the Gauss-Legendre numerical integration, the problem converts to a system of algebraic equations.

Keywords:

Distributed , order fractional differential equations , Beta function , Fractional integral operator , Collocation method