{"id":"W1989317524","doi":"10.1007/bf02832299","title":"Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution","year":2007,"lang":"en","type":"article","venue":"Journal of Applied Mathematics and Computing","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":158,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Fractional calculus; Laplace transform; Differentiable function; Partial derivative; Mathematical analysis; Derivative (finance); Chain rule (probability); Taylor series; Partial differential equation; Applied mathematics","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":[0.002117619,0.001173507,0.001322227,0.002133705,0.0009993345,0.002131557,0.001820023,0.002485692,0.003091089],"category_scores_gemma":[0.004782028,0.0004866692,0.001380866,0.001303743,0.00208752,0.003422654,0.002154378,0.00302159,0.0005391347],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001262926,"about_ca_system_score_gemma":0.001004546,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001374294,"about_ca_topic_score_gemma":0.00164332,"domain_scores_codex":[0.9995918,0.0001875677,0.00003174665,0.00004714906,0.0001175802,0.00002420052],"domain_scores_gemma":[0.9991054,0.0003874162,0.000100721,0.0000998226,0.0002254866,0.00008117023],"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":[0.00005021255,0.00004763368,0.0002117403,0.0001432611,0.00004630038,0.00007962548,0.000152521,0.01686075,0.002928984,0.9509623,0.001799641,0.02671702],"study_design_scores_gemma":[0.00003201949,0.00003706344,0.0002470223,0.00004770376,0.00004941454,0.0001501539,0.00005030197,0.5352927,0.001173092,0.4464011,0.01647585,0.0000435157],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01557944,0.005181096,0.9627608,0.001332322,0.001524713,0.00005394395,0.00006263333,0.0001142428,0.01339085],"genre_scores_gemma":[0.3498667,0.007533574,0.5495416,0.000979644,0.002488008,0.0004412977,0.0002138578,0.0004170105,0.08851838],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.003091089,"threshold_uncertainty_score":0.01119918,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03288480405294927,"score_gpt":0.3570328299983564,"score_spread":0.3241480259454071,"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."}}