{"id":"W4224138559","doi":"10.1186/s13662-022-03705-9","title":"Existence of solutions for a class of nonlinear fractional difference equations of the Riemann–Liouville type","year":2022,"lang":"en","type":"article","venue":"Advances in Continuous and Discrete Models","topic":"Nonlinear Differential Equations Analysis","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"Taif University; Ministerio de Ciencia, Innovación y Universidades","keywords":"Mathematics; Uniqueness; Nonlinear system; Class (philosophy); Type (biology); Mistake; Fractional calculus; Fixed-point theorem; Mathematical analysis; Set (abstract data type); Space (punctuation); Pure mathematics; Applied mathematics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001113636,0.0005950547,0.0007223602,0.000889966,0.0008787496,0.001259845,0.0007055609,0.001434186,0.001105754],"category_scores_gemma":[0.002394741,0.0002491306,0.001047233,0.0004758593,0.001879433,0.001126343,0.001171087,0.001104345,0.00007547149],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008081371,"about_ca_system_score_gemma":0.0005589465,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001092783,"about_ca_topic_score_gemma":0.0004292322,"domain_scores_codex":[0.9997017,0.0000841045,0.00002270448,0.00005193277,0.0000933168,0.00004622959],"domain_scores_gemma":[0.9994498,0.0002541463,0.0001034629,0.00003063785,0.0001117158,0.00005020614],"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":[0.000105065,0.0000966987,0.002793283,0.0002038454,0.00008701211,0.001102526,0.0006935633,0.0956215,0.03605417,0.8489539,0.0007732688,0.01351522],"study_design_scores_gemma":[0.0000512662,0.0001015569,0.000740808,0.00003557319,0.00002553703,0.0004741916,0.0002256113,0.773868,0.007929498,0.2144428,0.002063188,0.00004202522],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4361271,0.0008270664,0.5493648,0.001147752,0.0001686361,0.00008540464,0.00007245848,0.00007245531,0.01213439],"genre_scores_gemma":[0.9547735,0.0003864244,0.0404081,0.00008347019,0.00005060232,0.00008679691,0.00004507287,0.00001280868,0.004153127],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.001434186,"threshold_uncertainty_score":0.005889535,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05495162732405964,"score_gpt":0.3260122796633172,"score_spread":0.2710606523392576,"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."}}