On a numerical scheme for solving differential equations of fractional order

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A discrete method to solve fractional optimal control problems (2014, methodology): “To address this problem, a second approach was carried out in [2, 12], where a good approximation is obtained without the requirement of such higher-order smoothness on the admissible functions.”
A Caputo fractional derivative of a function with respect to another function (2016, methodology): “This was already done for the Riemann–Liouville and Caputo fractional operators [3, 6], and for the Hadamard fractional operators [5].”
Fractional differential equations with dependence on the Caputo-Katugampola derivative (2016, methodology): “Under the assumption that the set of admissible functions is C(2)([1, 2]) we can replace the fractional operator by the formula given in Theorem 8: D 1+ x(t) ≈ AN (t ρ − 1)tx(t)− N”
Fractional order optimal control problems with free terminal time (2013, methodology): “Nevertheless, we use approximations (1) and (2), up to order N , that have been introduced in [5] and used in [10, 21].”