In this paper a method for the numerical solution of distributed order FDEs (fractional
differential equations) of a general form is presented. The method applies to both linear and
nonlinear equations. The Caputo type fractional derivative is employed. The distributed
order FDE is approximated with a multi-term FDE, which is then solved by adjusting
appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several
example equations are solved and the response of mechanical systems described by such …

In this paper, a new numerical method for solving the distributed fractional differential
equations is presented. The method is based upon hybrid functions approximation. The
properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials
are presented. The Riemann–Liouville fractional integral operator for hybrid functions is
introduced. This operator is then utilized to reduce the solution of the distributed fractional
differential equations to a system of algebraic equations. Illustrative examples are included …