{"id":"W3212623749","doi":"10.3390/fractalfract5040200","title":"Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application","year":2021,"lang":"en","type":"article","venue":"Fractal and Fractional","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brandon University","funders":"Natural Sciences and Engineering Research Council of Canada; Prince Sultan University","keywords":"Fixed-point theorem; Mathematics; Nonlinear system; Stability (learning theory); Differential equation; Applied mathematics; Fixed point; Mathematical analysis; Computer science; Physics","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":[],"consensus_categories":[],"category_scores_codex":[0.0001556749,0.0001846542,0.0002801483,0.00009086014,0.0003818481,0.00005017399,0.00006088844,0.0001269248,0.0002072844],"category_scores_gemma":[0.0004180999,0.0001684175,0.00008964357,0.0001904482,0.0001891616,0.0003703004,0.00006413273,0.0002072499,0.000005519618],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001051895,"about_ca_system_score_gemma":0.0002287804,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008357151,"about_ca_topic_score_gemma":0.0001846616,"domain_scores_codex":[0.9984765,0.00006311389,0.000424763,0.0004045049,0.0004517735,0.000179339],"domain_scores_gemma":[0.9970426,0.001632617,0.0002824593,0.0002203303,0.0007128277,0.0001091958],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0005133168,0.001537025,0.004452731,0.000569522,0.0003553892,0.000002306457,0.0002714446,0.00006823576,0.01256488,0.9770005,0.0002658168,0.002398845],"study_design_scores_gemma":[0.007502598,0.0007431238,0.2141539,0.0004810542,0.001479736,0.0006865161,0.006112903,0.4793668,0.01182036,0.2633509,0.01251318,0.001788885],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3266762,0.00007149856,0.6708521,0.000610413,0.0001554455,0.0004264336,0.000616485,0.00005457893,0.0005369026],"genre_scores_gemma":[0.9645557,0.000009243564,0.03418721,0.00003312857,0.0002533517,0.0002673005,0.0004561622,0.0000222781,0.0002156295],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7136496,"threshold_uncertainty_score":0.6867867,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05452750495006972,"score_gpt":0.300570806589869,"score_spread":0.2460433016397993,"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."}}