New recursive approximations for variable-order fractional operators with applications

• Published in: Mathematical modelling and analysis Vol. 23; no. 2; pp. 227 - 239
• Main Authors: Zaky, Mahmoud A., Doha, Eid H., Taha, Taha M., Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 18.04.2018
• Subjects: Approximation; Bagley-Torvik equation; Boundary value problems; Collocation methods; Mathematical analysis; Mathematical research; modified generalized Laguerre polynomials; Operators (mathematics); Polynomials; spectral collocation methods; variable order fractional integrals and derivatives; Bagley-Torvik equation; modified generalized Laguerre polynomials; spectral collocation methods; variable order fractional integrals and derivatives
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/mma.2018.015

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.