Solving Time-Fractional Nonlinear Partial Differential Equations that Arise in the Biological Populations’ Spatial Diffusion Under Caputo-Katugampola Memory
Bibliographic record
Abstract
Using the Homotopy Perturbation Laplace Transform Method (HPLTM), the objective of our current work is to find the analytical solution of the nonlinear fractional partial differential equations arising in the spatial diffusion model of biological populations.This is achieved by replacing the Caputo fractional derivative of the Riemann-Liouville model with the Catogambola fractional derivative represented in the Caputo type.Moreover, the homotopy perturbation transform technique integrates the Laplace transform with the homotopy perturbation method.In addition, the efficiency of the proposed method is verified through three test examples.Accordingly, the results obtained by applying the proposed method for different fractional orders are plotted, and a comparative analysis is performed between our results and those of previous studies.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".