On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling
Why this work is in the frame
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Bibliographic record
Abstract
Abstract It has been pointed out that the derivative chains rules in fractional differential calculus via fractional calculus are not quite satisfactory as far as they can yield different results which depend upon how the formula is applied, that is to say depending upon where is the considered function and where is the function of function. The purpose of the present short note is to display some comments (which might be clarifying to some readers) on the matter. This feature is basically related to the non-commutativity of fractional derivative on the one hand, and furthermore, it is very close to the physical significance of the systems under consideration on the other hand, in such a manner that everything is right so. As an example, it is shown that the trivial first order system may have several fractional modelling depending upon the way by which it is observed. This suggests some rules to construct the fractional models of standard dynamical systems, in as meaningful a model as possible. It might happen that this pitfall comes from the feature that a function which is continuous everywhere, but is nowhere differentiable, exhibits random-like features.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it