Abstract
Functional differential equations have been widely used for modeling real-world phenomena in distinct areas of science. However, classical calculus can not provide always the best description of some complex phenomena, namely those observed in biological systems and medicine. This paper proposes a new numerical method for solving variable order fractional functional differential equations (VO-FFDE). Firstly, the shifted fractional Jacobi collocation method (SF-JC) is applied to solve the VO-FFDE with initial conditions. Then, the SF-JC is applied to the VO-FFDE with boundary conditions. Several numerical examples with different types of VO-FFDE demonstrate the superiority of the proposed method.