{"id":"W4415914275","doi":"10.28924/2291-8639-23-2025-285","title":"Integrable and Continuous Solutions of the Nonlinear Delayed Abel Fractal Integral Equation of the Second Kind","year":2025,"lang":"","type":"article","venue":"International Journal of Analysis and Applications","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Integrable system; Fractal; Nonlinear system; Stability (learning theory); Integral equation","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001175799,0.0002149311,0.0005966523,0.0005978856,0.0003167255,0.0001011586,0.0007996512,0.0001529945,0.0001967575],"category_scores_gemma":[0.001085584,0.0001407755,0.0007209787,0.001629487,0.0006690223,0.0002330697,0.0003364648,0.0005176565,9.554886e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001537458,"about_ca_system_score_gemma":0.0004967246,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002070668,"about_ca_topic_score_gemma":0.0009155036,"domain_scores_codex":[0.9966989,0.0002149921,0.001891909,0.0002527865,0.0007800529,0.0001613391],"domain_scores_gemma":[0.9927394,0.001354154,0.002282265,0.0004945552,0.003062728,0.00006688802],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001178633,0.006819624,0.09862448,0.0006145126,0.04575057,0.000001907778,0.00487933,0.007580189,0.03254317,0.739364,0.002844678,0.05979893],"study_design_scores_gemma":[0.007581438,0.0005731442,0.2026033,0.00186803,0.02748527,0.0001594253,0.0112583,0.2698097,0.02640809,0.4238282,0.02744332,0.000981792],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7210575,0.001398003,0.2643453,0.008620674,0.0005635383,0.0008158702,0.00125498,0.000006302668,0.001937881],"genre_scores_gemma":[0.9949451,0.000179106,0.003250343,0.0001004933,0.0001204258,0.00002249649,0.00002036537,0.000009842595,0.001351823],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3155358,"threshold_uncertainty_score":0.5740657,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01755545277508941,"score_gpt":0.2912814097899917,"score_spread":0.2737259570149023,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}