Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

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Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line (2014, methodology): “…Connolly, 2009) D2uðxÞ þD34uðxÞ þ uðxÞ ¼ x3 þ 6 xþ 8:533333333 x 2:25 ð0:25Þ , x 2 ½0, 1 , uð0Þ ¼ 0, u0ð0Þ ¼ 0, which has solution uðxÞ ¼ x3: This problem was investigated by Ford and Connolly (2009) using three decomposition methods, (for more details about these three methods, see Diethelm…”
Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials (2014, background): “Example 4 Our fourth example covers the inhomogeneous linear equation [55, 56] D2y.”
A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations (2011, background): “[26] and Ford and Connolly [27], where they transferred the problem to a system of fractional differential equations, each of order at most unity.”