Numerical methods for solving a part of fractional models

Fractional derivative operator is used by some of mathematicians for modeling and simulating many systems and processors based on the description of their properties . The main advantage of fractional derivatives in comparison with classical models with integer order is modeling many mechanical and electrical phenomena . One of these phenomena is fractional advection dispersion model (FADM) . The present study investigates 5 classes of these models . Methods for solving these models are presented using Caputo fractional derivatives , Riemann-Lioville and Riesz . These methods are classified into two sections : numerical and analytic . The present study mainly focuses on numerical methods . The implicit numerical methods attracted more attention . Examples are solved using MATLAB . These methods are unconditionally stable and convergent

Keywords:

Fractional differential equation , Implicit numerical methods , Stability , Convergence