{"id":"W4408822061","doi":"10.3390/fractalfract9040200","title":"Applications of Inverse Operators to a Fractional Partial Integro-Differential Equation and Several Well-Known Differential Equations","year":2025,"lang":"en","type":"article","venue":"Fractal and Fractional","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary; Brandon University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Differential equation; First-order partial differential equation; Inverse; Mathematical analysis; Integro-differential equation; Applied mathematics","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001809824,0.0003382177,0.0004113826,0.0006479239,0.0006890823,0.0001230006,0.0001639671,0.0002517134,0.002057297],"category_scores_gemma":[0.0006401013,0.0003428388,0.0001558597,0.0006080868,0.000248661,0.0005957538,0.0001952666,0.0004869536,0.00007385141],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001714281,"about_ca_system_score_gemma":0.0002689358,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002538034,"about_ca_topic_score_gemma":0.0001671467,"domain_scores_codex":[0.9976271,0.0001349223,0.0007716602,0.0005647478,0.0005812586,0.0003203228],"domain_scores_gemma":[0.9974852,0.001279689,0.0002770977,0.000290867,0.0004331286,0.0002340162],"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":[0.0004805838,0.001861733,0.003023312,0.0001598002,0.0005849093,0.000001593064,0.000467947,0.0007277802,0.01042043,0.9627873,0.00970225,0.009782377],"study_design_scores_gemma":[0.006853625,0.0006246064,0.1282272,0.0004968919,0.001656979,0.00008299444,0.002029665,0.3727708,0.004995391,0.3701447,0.1097812,0.002335886],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1641941,0.0000410641,0.8308799,0.001456203,0.0006673645,0.0007582628,0.0002259413,0.00009428591,0.001682868],"genre_scores_gemma":[0.990783,0.00002631659,0.005413561,0.0001994124,0.0004655483,0.0004984286,0.0003236426,0.00002790333,0.00226218],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8265889,"threshold_uncertainty_score":0.9999024,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03000914170773142,"score_gpt":0.3003403322471385,"score_spread":0.270331190539407,"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."}}