Inspired by JmsNxn's thread (http://math.eretrandre.org/tetrationforu...39#pid7139) about the continuum sum I repost this obsevation about the link between the fractional calculus and the Hyperoperations.
I guess that there can be interesting links... and probably is not the wrong way to approach the problem. I just found some results about something similar.
M. Campagnolo, C. Moore -Upper and Lower Bounds on
Continuous-Time Computation
In this text I found a relation betwen a hierarchy of real valued function and the Grzegorczyk hierarchy.
The interesting relations are betwen a hierarchy called
and the hierarchy
:
-------------------
The interesting thing is that the various levels of
are defined via iterated solution of a special kind of functional equation...and that maybe can be linked with your knowledge in this field...
Definition-
is defined as follow
and
if
if
I guess that there can be interesting links... and probably is not the wrong way to approach the problem. I just found some results about something similar.
M. Campagnolo, C. Moore -Upper and Lower Bounds on
Continuous-Time Computation
In this text I found a relation betwen a hierarchy of real valued function and the Grzegorczyk hierarchy.
The interesting relations are betwen a hierarchy called
Quote:1-Any function inis computable in
2-Ifthen
is the extension to the reals of some
then
3-the converse holds: ifis a function on the naturals of rank
it has an extension in
-------------------
The interesting thing is that the various levels of
Definition-
Quote:I-the constantsin a recursive way we define,
,
and
, the projection functions,
are in
II-is closed composition and linear integration
Quote:III-contains the functions in
![]()
IV-in we can find all the solutions to the equation (2) in this text ( http://languagelog.ldc.upenn.edu/myl/DK/...oMoore.pdf ) applied to the functions in
![]()
V-is closed under composition and linear integration
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