Fractional high order methods for the nonlinear fractional ordinary differential equation

By R. Lin, Fawang Liu. 2007

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Non-Differentiable Exact Solutions for the Nonlinear ODEs Defined on Fractal Sets (2017, unknown): “(18) and (19), we have Dφ1 tanτ (φ1μ ) = φ1φ2 ( 1 + tan(2)τ (φ2μ τ ) ) (20) and Dφ1 cotτ (φ2μ ) = −φ1φ2 ( 1 + cot(2)τ (φ2μ τ ) ) (21) so that”
Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations (2013, background): “For this reason fractional differential equations (FDE) have been considered by many authors and some numerical methods have proposed[2, 3, 4].”
New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation (2008, background): “Lin and Liu [24] proposed the high order (2-6) approximations of the fractional ordinary differential equation and discussed the consistency, convergence and stability of these fractional high order methods.”
Analytical solution for the time-fractional telegraph equation by the method of separating variables (2008, background): “Keywords: Fractional telegraph equation; Multivariate Mittag-Leffler function; Method of separating variables 1.”
The Finite Difference Methods for Fractional Ordinary Differential Equations (2013, methodology): “13), Lin and Liu [16] established a high-order method p-HOFLMSM for (1.”