{"id":"W3201136098","doi":"10.3390/fractalfract5030131","title":"Some Dynamical Models Involving Fractional-Order Derivatives with the Mittag-Leffler Type Kernels and Their Applications Based upon the Legendre Spectral Collocation Method","year":2021,"lang":"en","type":"article","venue":"Fractal and Fractional","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Legendre polynomials; Mathematics; Fractional calculus; Algebraic equation; Applied mathematics; Spectral method; Legendre wavelet; Nonlinear system; Collocation (remote sensing); Associated Legendre polynomials; Collocation method; Jacobi polynomials; Mathematical analysis; Differential equation; Orthogonal polynomials; Gegenbauer polynomials; Classical orthogonal polynomials; Ordinary differential equation; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004061985,0.0006356548,0.0007090839,0.0007449477,0.0006484365,0.0009627733,0.0008652098,0.001406043,0.0009707808],"category_scores_gemma":[0.0009735879,0.000271866,0.001188637,0.0005801758,0.0009399407,0.001479595,0.0005849776,0.0008315694,0.0001478162],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008704988,"about_ca_system_score_gemma":0.0006565521,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004461125,"about_ca_topic_score_gemma":0.002469071,"domain_scores_codex":[0.9997941,0.00005064945,0.00001130311,0.00003271169,0.00007375998,0.00003748036],"domain_scores_gemma":[0.9997095,0.0001004762,0.00006516229,0.00004029918,0.00006137605,0.00002306603],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003749426,0.00006993717,0.001071538,0.0001197826,0.00003799032,0.0003321344,0.0002115878,0.5491684,0.01148017,0.4263328,0.0009162215,0.01022191],"study_design_scores_gemma":[0.000003354491,0.000009276898,0.0001093641,0.000005078058,0.000005088695,0.00004807871,0.00001186549,0.9832324,0.0006978586,0.01521963,0.000647597,0.00001039841],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1255957,0.001388287,0.8534773,0.0006050218,0.0001751281,0.00006859699,0.0001075797,0.0002006392,0.01838179],"genre_scores_gemma":[0.9427214,0.0008041884,0.04830633,0.00009398576,0.00005964534,0.00007566818,0.00007345702,0.0000353633,0.007830041],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004461125,"threshold_uncertainty_score":0.008870363,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0425348736303593,"score_gpt":0.3016000656554012,"score_spread":0.2590651920250419,"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."}}