{"id":"W2793165349","doi":"10.3390/math6030032","title":"Babenko’s Approach to Abel’s Integral Equations","year":2018,"lang":"en","type":"article","venue":"Mathematics","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brandon University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Laplace transform; Integral equation; Fractional calculus; Convergence (economics); Operational calculus; Mathematical analysis; Calculus (dental); Summation equation; Series (stratigraphy); Laplace's equation; Applied mathematics; Partial differential equation","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003610043,0.0002190965,0.0002735725,0.0002477016,0.0003572487,0.00009132514,0.000345189,0.0001075173,0.0005255594],"category_scores_gemma":[0.002541806,0.0001986493,0.0001198492,0.0005767973,0.0001296817,0.0001554878,0.0001218729,0.0001817559,0.002099945],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001547558,"about_ca_system_score_gemma":0.00007924296,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001958212,"about_ca_topic_score_gemma":0.0000613101,"domain_scores_codex":[0.9983401,0.00005008238,0.0005087148,0.0002777753,0.000467846,0.0003554934],"domain_scores_gemma":[0.9980141,0.0006521661,0.0001416505,0.0006516274,0.0003627038,0.0001777491],"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":[0.000003346529,0.0007348021,0.000007172137,0.00004630782,0.00004573319,2.348513e-7,0.002105657,0.00001819486,0.0005003256,0.9769652,0.01909765,0.0004753116],"study_design_scores_gemma":[0.0003329913,0.0001284167,0.0001866143,0.00008739201,0.0001308478,0.00001778798,0.001148408,0.06445539,0.00082976,0.9272864,0.004959217,0.0004367687],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01645317,0.000005272158,0.8679452,0.0005229799,0.0002873877,0.0005214925,0.00003124942,0.0002706935,0.1139625],"genre_scores_gemma":[0.4679018,6.740646e-7,0.5263789,0.0001617445,0.0003265113,0.0001514833,0.00002388521,0.0000484717,0.005006552],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.4514486,"threshold_uncertainty_score":0.998677,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1407688487291179,"score_gpt":0.3625700743496901,"score_spread":0.2218012256205722,"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."}}