New recursive approximations for variable-order fractional operators with applications - Zaky, Mahmoud A.; Doha, Eid H.; Taha, Taha M.; Baleanu, Dumitru (Mathematical modelling and analysis, 2018)
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.