System initial conditions vs derivative initial conditions

Revisiting the 1D and 2D Laplace Transforms

“…This book became very popular and somehow imposed the ULT as a "standard" tool for solving constant coefficient differential equations. We can say that it is "the" LT for most mathematicians and scientists, even if it poses difficulties in the initial valued problems [12][13][14].…”

“…Gives a justification for Heaviside's operations, while giving insights into generalizations to the fractional case [13], 3.…”

Modified optimal energy and initial memory of fractional continuous-time linear systems

“…where according with many authors the condition a = I 1−α 0+ ϕ(t) t=0 is considered a technical initial condition, mainly due to the Laplace transform and without a good physical interpretation [6,7,8,9,14,15,16,17,22,23,24,28].…”

“…The initial condition problem for fractional linear systems is a subject under strong consideration [14,15,16,17,22,23,24,28]. Several authors claim that the Riemann-Liouville derivative leads to initial conditions without physical meaning.…”

Numerical analysis of the initial conditions in fractional systems

“…One of the difficulties often found by researchers consists of the initialization of fractional differential equations. In fact, while classical integer order systems require a finite set of initial conditions, fractional operators have an intrinsic memory of the phenomena that is translated into the requirement for a proper initialization and, eventually, to an infinite set of initial conditions [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. The problem becomes even more intricate when we verify that there are several possible definitions for the fractional operators, that may lead to the requirement either of integer or of fractional order initial conditions.…”