{"id":"https://openalex.org/W2075223383","doi":"https://doi.org/10.1007/s00500-011-0743-y","title":"Explicit solutions of fractional differential equations with uncertainty","display_name":"Explicit solutions of fractional differential equations with uncertainty","publication_year":2011,"publication_date":"2011-06-17","ids":{"openalex":"https://openalex.org/W2075223383","doi":"https://doi.org/10.1007/s00500-011-0743-y","mag":"2075223383"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-011-0743-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-011-0743-y","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073095019","display_name":"Tofigh Allahviranloo","orcid":"https://orcid.org/0000-0002-6673-3560"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"T. Allahviranloo","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","Islamic Azad University, Department of Mathematics, Science and Research Branch, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]},{"raw_affiliation_string":"Islamic Azad University, Department of Mathematics, Science and Research Branch, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085181870","display_name":"Soheil Salahshour","orcid":"https://orcid.org/0000-0003-1390-3551"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"S. Salahshour","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","Islamic Azad University, Department of Mathematics, Science and Research Branch, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]},{"raw_affiliation_string":"Islamic Azad University, Department of Mathematics, Science and Research Branch, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056670112","display_name":"S. Abbasbandy","orcid":"https://orcid.org/0000-0003-3385-4152"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"S. Abbasbandy","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","Islamic Azad University, Department of Mathematics, Science and Research Branch, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]},{"raw_affiliation_string":"Islamic Azad University, Department of Mathematics, Science and Research Branch, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073095019"],"corresponding_institution_ids":["https://openalex.org/I155419210"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":8.213,"has_fulltext":false,"cited_by_count":263,"citation_normalized_percentile":{"value":0.98111134,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"16","issue":"2","first_page":"297","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7838925123214722},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7814791798591614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.768295407295227},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6512736082077026},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6432632207870483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.478061705827713},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4564433693885803},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.42301711440086365},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.41094788908958435},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39957505464553833},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36292555928230286},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06823146343231201}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7838925123214722},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7814791798591614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.768295407295227},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6512736082077026},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6432632207870483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.478061705827713},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4564433693885803},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.42301711440086365},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.41094788908958435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39957505464553833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36292555928230286},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06823146343231201},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00500-011-0743-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-011-0743-y","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W626737487","https://openalex.org/W1552110944","https://openalex.org/W1584611818","https://openalex.org/W1986374161","https://openalex.org/W1997679081","https://openalex.org/W2000348782","https://openalex.org/W2011301580","https://openalex.org/W2046831675","https://openalex.org/W2055257218","https://openalex.org/W2056258420","https://openalex.org/W2060759268","https://openalex.org/W2065268523","https://openalex.org/W2070545443","https://openalex.org/W2077430350","https://openalex.org/W2138412914","https://openalex.org/W2324258602","https://openalex.org/W2483918881","https://openalex.org/W2787959293","https://openalex.org/W4232482330"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W1604739066","https://openalex.org/W2115878407","https://openalex.org/W2043671984"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":20},{"year":2023,"cited_by_count":31},{"year":2022,"cited_by_count":28},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":7}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
