Solutions of nonlinear Murray equation for blood flow in vessels by Laplace-residual power series
Bibliographic record
Abstract
Purpose This study aims to introduce a novel hybrid approach called the Laplace-Residual Power Series Method (L-RPSM) for solving fractional nonlinear problems, specifically the Murray differential equation. This method combines the Residual Power Series Method (RPSM) with the Laplace Transform (LT). Design/methodology/approach The L-RPSM is applied to fractional nonlinear problems, including the Murray equation. The method provides an efficient means of obtaining exact and approximate series solutions for fractional differential equations. Numerical and graphical results are computed for different values of the fractional order parameter μ using Mathematica software. The performance and solutions of L-RPSM are compared with other established methods (Bernoulli wavelet collocation and reduced differential transform method) to demonstrate its effectiveness. Findings The L-RPSM successfully solves two cases of the Murray equation. The results demonstrate that the proposed approach is simple, accurate, and broadly applicable. The numerical and graphical results illustrate the behavior of the L-RPSM solutions and specifically show the influence of the fractional derivative (through parameter μ) on the obtained solutions. Originality/value The primary originality lies in the novel combination of the RPSM with the LT to form the L-RPSM specifically for tackling fractional nonlinear differential equations. The study provides clear evidence of the method's simplicity, accuracy, and broad applicability through solved examples and comparisons. Furthermore, it visually demonstrates the significant impact of the fractional order derivative on the solution behavior using 2D and 3D plots.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".