{"id":"https://openalex.org/W4306404442","doi":"https://doi.org/10.3390/sym14102168","title":"Fractional View Analysis of Emden-Fowler Equations with the Help of Analytical Method","display_name":"Fractional View Analysis of Emden-Fowler Equations with the Help of Analytical Method","publication_year":2022,"publication_date":"2022-10-16","ids":{"openalex":"https://openalex.org/W4306404442","doi":"https://doi.org/10.3390/sym14102168"},"language":"en","primary_location":{"id":"doi:10.3390/sym14102168","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102168","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2168/pdf?version=1666757079","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/10/2168/pdf?version=1666757079","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078096818","display_name":"Thongchai Botmart","orcid":"https://orcid.org/0000-0001-9325-5560"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Thongchai Botmart","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034707465","display_name":"Muhammad Naeem","orcid":"https://orcid.org/0000-0003-4755-9381"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Muhammad Naeem","raw_affiliation_strings":["Deanship of Joint First Year, Umm Al-Qura University, Makkah P.O. Box 715, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deanship of Joint First Year, Umm Al-Qura University, Makkah P.O. Box 715, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083354054","display_name":"Rasool Shah","orcid":"https://orcid.org/0000-0003-4306-8489"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Rasool Shah","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-4306-8489","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081449036","display_name":"Naveed Iqbal","orcid":"https://orcid.org/0000-0002-8548-7078"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Naveed Iqbal","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il P.O. Box 2440, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il P.O. Box 2440, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-8548-7078","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il P.O. Box 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il P.O. Box 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034707465","https://openalex.org/A5083354054"],"corresponding_institution_ids":["https://openalex.org/I181063083","https://openalex.org/I199693650"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.2379,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76721009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"10","first_page":"2168","last_page":"2168"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9395999908447266,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.8944973945617676},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7418038845062256},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6274056434631348},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5430566072463989},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.4535937011241913},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.45055297017097473},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44981247186660767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4339144825935364},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4322686195373535},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.428117573261261},{"id":"https://openalex.org/keywords/laplaces-equation","display_name":"Laplace's equation","score":0.4192239046096802},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.28506264090538025},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2599011957645416},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2245924174785614}],"concepts":[{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.8944973945617676},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7418038845062256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6274056434631348},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5430566072463989},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.4535937011241913},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.45055297017097473},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44981247186660767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4339144825935364},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4322686195373535},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.428117573261261},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.4192239046096802},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28506264090538025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2599011957645416},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2245924174785614},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14102168","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102168","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2168/pdf?version=1666757079","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:dc8bd7f6bd52439da0e0cbf86aa56a16","is_oa":true,"landing_page_url":"https://doaj.org/article/dc8bd7f6bd52439da0e0cbf86aa56a16","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 10, p 2168 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/10/2168/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14102168","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14102168","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102168","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2168/pdf?version=1666757079","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4306404442.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W433794350","https://openalex.org/W1850511188","https://openalex.org/W1969004631","https://openalex.org/W1986738478","https://openalex.org/W2018307540","https://openalex.org/W2027361385","https://openalex.org/W2050407410","https://openalex.org/W2073721135","https://openalex.org/W2076228995","https://openalex.org/W2076235615","https://openalex.org/W2090867843","https://openalex.org/W2228432717","https://openalex.org/W2317731414","https://openalex.org/W2317826680","https://openalex.org/W2338497210","https://openalex.org/W2418430460","https://openalex.org/W2465700212","https://openalex.org/W2582926331","https://openalex.org/W2613510042","https://openalex.org/W2790754607","https://openalex.org/W2794917395","https://openalex.org/W2801192398","https://openalex.org/W2864245334","https://openalex.org/W2946444571","https://openalex.org/W2950396773","https://openalex.org/W2953878459","https://openalex.org/W2970104767","https://openalex.org/W2972177571","https://openalex.org/W3011367397","https://openalex.org/W3024042440","https://openalex.org/W3041281016","https://openalex.org/W3098017255","https://openalex.org/W3161173475","https://openalex.org/W3163715634","https://openalex.org/W3182952698","https://openalex.org/W3188219998","https://openalex.org/W3192786276","https://openalex.org/W3193563979","https://openalex.org/W3199183383","https://openalex.org/W3205232940","https://openalex.org/W3207401169","https://openalex.org/W3212952961","https://openalex.org/W4206290559","https://openalex.org/W4254735241","https://openalex.org/W4293558596","https://openalex.org/W6673343839","https://openalex.org/W6699843117","https://openalex.org/W6703386984","https://openalex.org/W6795182159","https://openalex.org/W6799693611","https://openalex.org/W6800862419","https://openalex.org/W6802647595"],"related_works":["https://openalex.org/W4313233315","https://openalex.org/W3095724723","https://openalex.org/W1586145079","https://openalex.org/W4281619695","https://openalex.org/W2901432230","https://openalex.org/W2048436983","https://openalex.org/W2233017382","https://openalex.org/W2523462812","https://openalex.org/W4317627639","https://openalex.org/W4401383466"],"abstract_inverted_index":{"This":[0],"work":[1],"aims":[2],"at":[3],"a":[4],"new":[5],"semi-analytical":[6],"technique":[7,39,57],"called":[8],"the":[9,14,24,31,34,41,68,71],"Adomian":[10],"decomposition":[11],"method":[12,26,73],"for":[13],"analysis":[15],"of":[16,33],"time-fractional":[17],"Emden\u2013Fowler":[18],"equations.":[19],"The":[20,37,55],"Laplace":[21],"transformation":[22],"and":[23,53],"iterative":[25],"are":[27],"implemented":[28],"to":[29,67],"obtain":[30],"result":[32],"given":[35],"models.":[36,65],"suggested":[38],"has":[40],"edge":[42],"over":[43],"other":[44,76],"methods,":[45],"as":[46],"it":[47],"does":[48],"not":[49],"need":[50],"extra":[51],"materials":[52],"calculations.":[54],"presented":[56],"validity":[58],"is":[59],"demonstrated":[60],"by":[61],"examining":[62],"four":[63],"mathematical":[64],"Due":[66],"straightforward":[69],"implementation,":[70],"proposed":[72],"can":[74],"solve":[75],"non-linear":[77],"fractional":[78],"order":[79],"problems.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
