{"id":"W2796942774","doi":"10.1088/1751-8121/aad345","title":"On generalized and fractional derivatives and their applications to classical mechanics","year":2018,"lang":"en","type":"article","venue":"Journal of Physics A Mathematical and Theoretical","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Fractional calculus; Differential operator; Operator (biology); Eigenvalues and eigenvectors; Motion (physics); Equations of motion; Generalized eigenvector; Central force; Harmonic oscillator; Differential equation","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":[0.0003120875,0.0001627459,0.0003269676,0.00007646161,0.0002020914,0.00006699118,0.00008359514,0.00007646165,0.0001417865],"category_scores_gemma":[0.0007210023,0.0001092575,0.00007012566,0.0001292108,0.000533985,0.0001076285,0.00008569078,0.0002438387,0.00001452764],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002470779,"about_ca_system_score_gemma":0.00003533345,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":1.669651e-7,"about_ca_topic_score_gemma":3.086648e-7,"domain_scores_codex":[0.9989478,0.00008643612,0.0003822684,0.0001669309,0.0002605694,0.0001560254],"domain_scores_gemma":[0.9973152,0.00191973,0.0001460039,0.0001309283,0.0002411674,0.000246972],"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":[0.00007106205,0.0003451671,0.000001719528,0.00002580515,0.00006748346,5.854359e-7,0.00031258,9.999367e-7,0.001380051,0.9951304,0.0001839001,0.002480227],"study_design_scores_gemma":[0.0003629266,0.0003648366,0.00004785576,0.00007136143,0.00006087107,0.00008646494,0.0001201361,0.008625186,0.0008552119,0.9890843,0.0002041039,0.0001167657],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2480837,0.00001685529,0.7488755,0.002299986,0.00003761382,0.0001788356,0.00001305889,0.00001283739,0.0004816125],"genre_scores_gemma":[0.9631099,0.00001361408,0.03617856,0.0002244116,0.0004036126,0.00002213529,0.00000103646,0.0000184719,0.00002829545],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7150261,"threshold_uncertainty_score":0.4455392,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03608320594987399,"score_gpt":0.3204640584024247,"score_spread":0.2843808524525507,"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."}}