{"id":"W2883208200","doi":"10.1016/j.cnsns.2018.07.035","title":"Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions","year":2018,"lang":"en","type":"article","venue":"Communications in Nonlinear Science and Numerical Simulation","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":134,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Fractional calculus; Mathematics; Series (stratigraphy); Power series; Semigroup; Product (mathematics); Connection (principal bundle); Applied mathematics; Calculus (dental); Algebra over a field; Pure mathematics; Mathematical analysis","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":[0.001577797,0.00154048,0.00111216,0.003198332,0.001164588,0.003896723,0.001580627,0.002579314,0.007512999],"category_scores_gemma":[0.004734299,0.0004127456,0.001350737,0.002384102,0.002741764,0.004467973,0.001701579,0.002576018,0.00137312],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001354133,"about_ca_system_score_gemma":0.0006884798,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008559945,"about_ca_topic_score_gemma":0.0006976121,"domain_scores_codex":[0.9994165,0.0002019627,0.00003681679,0.0000615988,0.0001913124,0.00009185953],"domain_scores_gemma":[0.9987665,0.0004739627,0.0001630078,0.0001819889,0.0002436124,0.0001709856],"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":[0.000026383,0.00002294095,0.00005410796,0.00003863733,0.000009882646,0.0001101371,0.0001547968,0.00411386,0.001785845,0.9885378,0.0005705054,0.004575014],"study_design_scores_gemma":[0.00001888203,0.00002249521,0.0001116883,0.00002165222,0.00001390315,0.0002053684,0.00008386322,0.1283652,0.001018966,0.8674901,0.002612061,0.00003582541],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1800461,0.002528572,0.7254837,0.00171168,0.001509801,0.00009730306,0.0001825915,0.0005848226,0.08785558],"genre_scores_gemma":[0.8691313,0.002190225,0.07130174,0.0006301287,0.001290465,0.00014567,0.0002333118,0.0004477611,0.05462937],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007512999,"threshold_uncertainty_score":0.02513343,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1416202009398115,"score_gpt":0.4314013336881285,"score_spread":0.289781132748317,"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."}}