Approximate Solutions of the Coupled M-Truncated Fractional mKdV System Using the Adomian Decomposition Technique
Bibliographic record
Abstract
This manuscript employs the Adomian decomposition technique (ADT) to develop solutions for the fractional space-time nonlinear mKdV system, incorporating an M-truncated fractional order and supposed initial conditions. The technique yields a power series expansion solution without the need for linearization, weak nonlinear assumptions, or perturbation theory. Software such as Maple or Mathematica was utilized to compute the Adomian formulas for the solution expansion. This technique can also be utilized for a range of nonlinear fractional-order models in mathematical physics. A graphical analysis is provided to demonstrate the behavior of Adomian solutions and how variations in non-integer order values influence the results. The technique is straightforward, clear, and widely applicable to other nonlinear fractional problems in both physics and mathematics. It is believed that these studies significantly advance our understanding of the nonlinear coupled fractional mKdV system and its potential applications in physics and engineering.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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 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".