{"id":"https://openalex.org/W4409269642","doi":"https://doi.org/10.3390/axioms14040282","title":"A Comprehensive Study of Nonlinear Mixed Integro-Differential Equations of the Third Kind for Initial Value Problems: Existence, Uniqueness and Numerical Solutions","display_name":"A Comprehensive Study of Nonlinear Mixed Integro-Differential Equations of the Third Kind for Initial Value Problems: Existence, Uniqueness and Numerical Solutions","publication_year":2025,"publication_date":"2025-04-08","ids":{"openalex":"https://openalex.org/W4409269642","doi":"https://doi.org/10.3390/axioms14040282"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14040282","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040282","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms14040282","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022849085","display_name":"Ahmed S. Rahby","orcid":"https://orcid.org/0000-0003-1103-3652"},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN","EG"],"is_corresponding":true,"raw_author_name":"Ahmed S. Rahby","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt","School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt","institution_ids":["https://openalex.org/I207547235"]},{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088545047","display_name":"Sameh Askar","orcid":"https://orcid.org/0000-0002-1167-2430"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Sameh S. Askar","raw_affiliation_strings":["Department of Statistic and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Statistic and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018298333","display_name":"Ahmad M. Alshamrani","orcid":"https://orcid.org/0000-0001-7103-8872"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmad M. Alshamrani","raw_affiliation_strings":["Department of Statistic and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Statistic and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061048758","display_name":"Gamal A. Mosa","orcid":"https://orcid.org/0000-0001-9470-7549"},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Gamal A. Mosa","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt","institution_ids":["https://openalex.org/I207547235"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5022849085"],"corresponding_institution_ids":["https://openalex.org/I204983213","https://openalex.org/I207547235"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12086828,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"4","first_page":"282","last_page":"282"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9939000010490417,"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/uniqueness","display_name":"Uniqueness","score":0.8807935118675232},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6424363851547241},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6038640737533569},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5345790386199951},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5010662078857422},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.48507800698280334},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.475147008895874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46785905957221985},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19088762998580933},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.04842424392700195}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8807935118675232},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6424363851547241},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6038640737533569},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5345790386199951},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5010662078857422},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.48507800698280334},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.475147008895874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46785905957221985},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19088762998580933},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.04842424392700195},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14040282","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040282","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:dd07b0e36f3248cc91208297104b7f8f","is_oa":true,"landing_page_url":"https://doaj.org/article/dd07b0e36f3248cc91208297104b7f8f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 4, p 282 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14040282","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040282","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G945450247","display_name":null,"funder_award_id":"RSPD2025R533","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W7148150","https://openalex.org/W972249039","https://openalex.org/W1967997940","https://openalex.org/W1977207815","https://openalex.org/W1997299127","https://openalex.org/W2015922268","https://openalex.org/W2029095782","https://openalex.org/W2033864933","https://openalex.org/W2062850938","https://openalex.org/W2075151302","https://openalex.org/W2085538157","https://openalex.org/W2090518453","https://openalex.org/W2206410392","https://openalex.org/W2233214786","https://openalex.org/W2573944670","https://openalex.org/W2626192092","https://openalex.org/W2736521523","https://openalex.org/W2981758100","https://openalex.org/W3135175711","https://openalex.org/W3172688589","https://openalex.org/W4251623281","https://openalex.org/W4253452485","https://openalex.org/W4286001892","https://openalex.org/W4315784743","https://openalex.org/W4399543090","https://openalex.org/W4400782609","https://openalex.org/W4401183100","https://openalex.org/W6716768850"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W4386094278","https://openalex.org/W2050111419","https://openalex.org/W2898988421"],"abstract_inverted_index":{"Nonlinear":[0],"mixed":[1],"integro-differential":[2],"equations":[3],"(NM-IDEs)":[4],"of":[5,35,38,58,65,82],"the":[6,31,46,49,56,59,63,66,74,99],"third":[7],"kind":[8],"present":[9],"a":[10,36,80,102],"complex":[11],"challenge":[12],"during":[13],"solving":[14,89],"initial":[15],"value":[16],"problems":[17],"(IVPs),":[18],"particularly":[19],"after":[20],"converting":[21,93],"them":[22,94],"from":[23],"standard":[24],"forms.":[25],"In":[26],"this":[27],"work,":[28],"we":[29,44],"address":[30],"existence":[32],"and":[33,54,73,84,97],"uniqueness":[34],"type":[37],"NM-IDEs":[39,96],"employing":[40],"Picard\u2019s":[41],"method.":[42],"Additionally,":[43],"estimate":[45],"solution":[47],"using":[48,98],"homotopy":[50],"analysis":[51],"method":[52],"(HAM)":[53],"analyze":[55],"convergence":[57],"approach.":[60,105],"To":[61],"demonstrate":[62],"credibility":[64],"theoretical":[67],"results,":[68],"various":[69],"applications":[70],"are":[71,77],"given,":[72],"numerical":[75],"results":[76],"displayed":[78],"in":[79],"group":[81],"figures":[83],"tables":[85],"to":[86,95],"highlight":[87],"that":[88],"IVPs":[90],"by":[91],"first":[92],"HAM":[100],"is":[101],"computationally":[103],"efficient":[104]},"counts_by_year":[],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}