{"id":"W4388636878","doi":"10.3390/axioms12111046","title":"Complex Generalized Representation of Gamma Function Leading to the Distributional Solution of a Singular Fractional Integral Equation","year":2023,"lang":"en","type":"article","venue":"Axioms","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"Majmaah University","keywords":"Dirac delta function; Mathematics; Gamma function; Laplace transform; Fractional calculus; Singularity; Mittag-Leffler function; Function (biology); Generalized function; Pure mathematics; Integral equation; Gravitational singularity; Representation (politics); Power series; Series (stratigraphy); Mathematical analysis; Law","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":[0.0005120405,0.0001314237,0.0002288682,0.0003153,0.0002830215,0.00002234127,0.0001452569,0.00008339635,0.0003141862],"category_scores_gemma":[0.001536181,0.000114333,0.0001776013,0.001354015,0.0001056051,0.0002285701,0.00005161967,0.0001313423,0.0001428727],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001799497,"about_ca_system_score_gemma":0.00008131396,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003069798,"about_ca_topic_score_gemma":0.00009504982,"domain_scores_codex":[0.9980934,0.0001874041,0.0005990962,0.0002275077,0.0006895222,0.0002031266],"domain_scores_gemma":[0.9980528,0.0007401154,0.0003665446,0.0002926978,0.000498014,0.00004976327],"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":[0.0001730885,0.0001963958,0.0003471321,0.00003552856,0.000146928,4.105598e-7,0.0004288925,0.007727277,0.1577719,0.8188034,0.01131188,0.003057207],"study_design_scores_gemma":[0.001638041,0.0003386173,0.1895175,0.0001740444,0.0004058261,0.00001792034,0.00111344,0.4346468,0.02294855,0.3454955,0.003226143,0.0004776008],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2621809,0.000008643297,0.734883,0.001744817,0.000408983,0.0003474865,0.0001101521,0.00008591083,0.0002301716],"genre_scores_gemma":[0.994687,0.000004490013,0.003255893,0.00003458535,0.0001975325,0.00009688509,0.001284022,0.00001789133,0.000421677],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7325061,"threshold_uncertainty_score":0.4662365,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2122317348212927,"score_gpt":0.388560846171186,"score_spread":0.1763291113498933,"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."}}