Initialized Fractional Calculus

136 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Fractional systems state space description: some wrong ideas and proposed solutions (2014, background): “…that the response of the fractional-order system 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…”
A General Formulation and Solution Scheme for Fractional Optimal Control Problems (2004, background): “Lorenzo and Hartley [33] have discussed the problem of finding the correct form of the initial conditions in a more general setting.”
TUTORIAL ON SYSTEM IDENTIFICATION USING FRACTIONAL DIFFERENTIATION MODELS (2006, background): “Lorenzo and Hartley (2000) showed that the effect of the past can be considered by taking into account an initialization function instead of a limited number of points.”
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].”