  A simple yet effective numerical method using orthogonal hybrid functions
consisting of piecewise constant orthogonal sample-and-hold functions and
piecewise linear orthogonal triangular functions is proposed to solve
numerically fractional order non-stiff and stiff differential-algebraic
equations. The complementary generalized one-shot operational matrices, which
are the foundation for the developed numerical method, are derived to estimate
the Riemann-Liouville fractional order integral in the new orthogonal hybrid
function domain. It is theoretically and numerically shown that the numerical
method converges the approximate solutions to the exact solution in the limit
of step size tends to zero. Numerical examples are solved using the proposed
method and the obtained results are compared with the results of some popular
semi-analytical techniques used for solving fractional order
differential-algebraic equations in the literature. Our results are in good
accordance with the results of those semi-analytical methods in case of
non-stiff problems and our method provides valid approximate solution to stiff
problem (fractional order version of Chemical Akzo Nobel problem) which those
semi-analytical methods fails to solve.
