A New Fixed Point Approach for Approximating Solutions of Fractional Differential Equations in Banach Spaces
Bibliographic record
Abstract
This contribution targets the solution of fractional differential equations (FDEs) via novel iterative approach and in a new class of nonlinear mappings. Our approach is based on the class of (α, β, γ)-nonexpansive mappings and three-step M-iterative scheme. Under various assumptions, we first carry out some weak and strong convergence results in a setting of a Banach spaces. After this, we carry out an application of one our main result to find approximate solution for a broad class of FDEs. Eventually, we we construct a new example of (α, β, γ)-nonexpansive mappings and show that this new mapping is not continuous on its whole domain and hence it is not nonexpansive. Using this example, we perform a numerical simulation of various iterative scheme including our M-iterative scheme. It has been observed the numerical effectiveness of the M-iterative scheme is high as compared to the other iterative schemes. Accordingly, our main outcome is new/extends some known results of the literature.
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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 | 0.001 |
| 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".