Numerical Method for Fractional-order Problems Using MATLAB software

Abstract

Solving of Fractional differential equations of fractional (i.e., non-integer) order in an accurate, reliable and efficient way is much more difficult than in the standard integer-order case; moreover, the majority of the computational tools do not provide built-in functions for this kind of problem. In this paper was included the effective families of numerical methods for fractional-order problems, and the major computational issues such as the efficient treatment of the persistent memory term and the solution of the nonlinear systems involved in implicit methods using MATLAB routines specifically devised for solving three families of fractional-order problems: fractional differential equations (FDEs) (also for the non-scalar case), multi-order systems (MOSs) of FDEs and multi-term FDEs (also for the non-scalar case); some examples are provided to illustrate the use of the routines.