{"corpus_id":115290010,"paper_sha":"e0f45484c86874276c1f09caaa1066b5feac428e","doi":"10.1177/1461348419827378","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2911926389,"dblp_id":null,"acl_id":null,"title":"Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control","year":2019,"publication_date":"2019-02-12","venue":"Journal of Low Frequency Noise Vibration and Active Control","journal":{"name":"Journal of Low Frequency Noise, Vibration and Active Control","pages":"706 - 727","volume":"38"},"journal_issn":null,"journal_title":null,"publication_types":["JournalArticle"],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Engineering"],"reference_count":46,"citation_count":10,"influential_citation_count":1,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"This paper attempts to propose and investigate a modification of the homotopy perturbation method to study hypersingular integral equations of the first kind. Along with considering this matter, of course, the novel method has been compared with the standard homotopy perturbation method. This method can be conveniently fast to get the exact solutions. The validity and reliability of the proposed scheme are discussed. Different examples are included to prove so. According to the results, we further state that new simple homotopy perturbation method is so efficient and promises the exact solution. The modification of the homotopy perturbation method has been discovered to be the significant ideal tool in dealing with the complicated function-theoretic analytical structures within an analytical method.","claims":[{"public_id":"cl_7ac5ad02776c6784be74a3d4c96ea4b7","status":"active","text":"A modified homotopy perturbation method is proposed for hypersingular integral equations of the first kind.","confidence":0.98,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_7ac5ad02776c6784be74a3d4c96ea4b7"},{"public_id":"cl_097e33074c9e7e1187077ce65587887a","status":"active","text":"The method is reported to obtain exact solutions quickly and efficiently on the included examples.","confidence":0.91,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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