  To broaden the range of applicability of variable-order fractional
differential models, reliable numerical approaches are needed to solve the
model equation. In this paper, we develop Laguerre spectral collocation methods
for solving variable-order fractional initial value problems on the half line.
Specifically, we derive three-term recurrence relations to efficiently
calculate the variable-order fractional integrals and derivatives of the
modified generalized Laguerre polynomials, which lead to the corresponding
fractional differentiation matrices that will be used to construct the
collocation methods. Comparison with other existing methods shows the superior
accuracy of the proposed spectral collocation methods.
