Initialization of Fractional-Order Operators and Fractional Differential Equations

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On some new properties of fractional derivatives with Mittag-Leffler kernel (2017, methodology): “We recall that the fractional integrator, as well as the related continuous frequency distributed differential model, represents an important tool for the simulation of fractional systems together with the solution of initial condition problems [23, 42, 43, 44].”
Quantum field theory, gravity and cosmology in a fractal universe (2010, background): “It should be easy to see that Λ can be regarded as the complementary function of initialized fractional calculus [35, 73, 74, 75].”
Fractional systems state space description: some wrong ideas and proposed solutions (2014, background): “…is the sum of a forced response and a response to initial conditions: y tð Þ ¼ yf tð Þ þ yi tð Þ ð38Þ In Lorenzo and Hartley (2000), Hartley and Lorenzo (2002), Lorenzo and Hartley (2008, 2011), it was demonstrated that the pseudo trajectories of the fractional system obtained with Caputo’s…”