{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004750339,0.0001139227,0.000257649,0.00004765205,0.0002527804,0.00005021202,0.00006209799,0.00003213753,0.00002245768],"category_scores_gemma":[0.00004216262,0.00009470688,0.0000667343,0.00007268551,0.00005192536,0.00006113255,0.00005151283,0.0001263038,5.246164e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001140566,"about_ca_system_score_gemma":0.00002691375,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001707273,"about_ca_topic_score_gemma":1.512859e-7,"domain_scores_codex":[0.9991426,0.000005355259,0.0004846813,0.0001048999,0.00009701672,0.0001654207],"domain_scores_gemma":[0.9978811,0.001373508,0.000471811,0.00006997005,0.00008912621,0.0001144435],"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":[0.00003391977,0.00009278972,0.000001750666,0.00002695319,0.00006128096,5.527637e-8,0.0006381511,0.0002594775,0.005234508,0.9342659,0.00003763824,0.05934763],"study_design_scores_gemma":[0.0007342041,0.00004318916,0.00001673464,0.00003664142,0.00007413228,0.000004052766,0.001156873,0.1583235,0.003509037,0.8351251,0.0008552546,0.0001212443],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01183409,0.00002883886,0.9860254,0.0001087785,0.00004843952,0.0002076523,0.000003851545,0.000007426369,0.00173555],"genre_scores_gemma":[0.4883091,0.000001455239,0.5113649,0.00001198233,0.0002833673,0.000003146738,0.00000295967,0.000008132723,0.00001497319],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.476475,"threshold_uncertainty_score":0.3862035,"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."}}