{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T00:49:59Z","timestamp":1782002999070,"version":"3.54.5"},"publisher-location":"Cham","reference-count":13,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783031087530","type":"print"},{"value":"9783031087547","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-08754-7_22","type":"book-chapter","created":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T03:06:09Z","timestamp":1655780769000},"page":"162-168","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pseudo-Newton Method with\u00a0Fractional Order Derivatives"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9434-9307","authenticated-orcid":false,"given":"Krzysztof","family":"Gdawiec","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0492-772X","authenticated-orcid":false,"given":"Agnieszka","family":"Lisowska","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5920-5161","authenticated-orcid":false,"given":"Wies\u0142aw","family":"Kotarski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,6,15]]},"reference":[{"key":"22_CR1","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1016\/j.aml.2019.06.028","volume":"98","author":"A Akg\u00fcl","year":"2019","unstructured":"Akg\u00fcl, A., Cordero, A., Torregrosa, J.: A fractional Newton method with $$2\\alpha $$th-order of convergence and its stability. Appl. Math. Lett. 98, 344\u2013351 (2019). https:\/\/doi.org\/10.1016\/j.aml.2019.06.028","journal-title":"Appl. Math. Lett."},{"key":"22_CR2","doi-asserted-by":"publisher","unstructured":"Cordero, A., Girona, I., Torregrosa, J.: A variant of Chebyshev\u2019s method with $$3\\alpha $$th-order of convergence by using fractional derivatives. Symmetry 11(8), Article 1017 (2019). https:\/\/doi.org\/10.3390\/sym11081017","DOI":"10.3390\/sym11081017"},{"issue":"10","key":"22_CR3","doi-asserted-by":"publisher","first-page":"2109","DOI":"10.1080\/00207160.2019.1683547","volume":"97","author":"R Erfanifar","year":"2020","unstructured":"Erfanifar, R., Sayevand, K., Esmaeili, H.: On modified two-step iterative method in the fractional sense: some applications in real world phenomena. Int. J. Comput. Math. 97(10), 2109\u20132141 (2020). https:\/\/doi.org\/10.1080\/00207160.2019.1683547","journal-title":"Int. J. Comput. Math."},{"key":"22_CR4","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.amc.2017.02.038","volume":"307","author":"K Gdawiec","year":"2017","unstructured":"Gdawiec, K., Kotarski, W.: Polynomiography for the polynomial infinity norm via Kalantari\u2019s formula and nonstandard iterations. Appl. Math. Comput. 307, 17\u201330 (2017). https:\/\/doi.org\/10.1016\/j.amc.2017.02.038","journal-title":"Appl. Math. Comput."},{"key":"22_CR5","doi-asserted-by":"publisher","unstructured":"Gdawiec, K., Kotarski, W., Lisowska, A.: Visual analysis of the Newton\u2019s method with fractional order derivatives. Symmetry 11(9), Article ID 1143 (2019). https:\/\/doi.org\/10.3390\/sym11091143","DOI":"10.3390\/sym11091143"},{"issue":"3","key":"22_CR6","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1007\/s11075-020-00919-4","volume":"86","author":"K Gdawiec","year":"2020","unstructured":"Gdawiec, K., Kotarski, W., Lisowska, A.: Newton\u2019s method with fractional derivatives and various iteration processes via visual analysis. Numer. Algorithms 86(3), 953\u20131010 (2020). https:\/\/doi.org\/10.1007\/s11075-020-00919-4","journal-title":"Numer. Algorithms"},{"issue":"10","key":"22_CR7","doi-asserted-by":"publisher","first-page":"931","DOI":"10.4169\/amer.math.monthly.118.10.931","volume":"118","author":"B Kalantari","year":"2011","unstructured":"Kalantari, B.: A geometric modulus principle for polynomials. Am. Math. Mon. 118(10), 931\u2013935 (2011). https:\/\/doi.org\/10.4169\/amer.math.monthly.118.10.931","journal-title":"Am. Math. Mon."},{"key":"22_CR8","unstructured":"Kalantari, B.: A necessary and sufficient condition for local maxima of polynomial modulus over unit disc. arXiv:1605.00621 (2016)"},{"key":"22_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11075-021-01208-4","volume":"3","author":"B Kalantari","year":"2021","unstructured":"Kalantari, B., Andreev, F., Lau, C.: Characterization of local optima of polynomial modulus over a disc. Numer. Algorithms 3, 1\u201315 (2021). https:\/\/doi.org\/10.1007\/s11075-021-01208-4","journal-title":"Numer. Algorithms"},{"key":"22_CR10","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"K Miller","year":"1993","unstructured":"Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons Inc., New York (1993)"},{"key":"22_CR11","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"S Samko","year":"1993","unstructured":"Samko, S., Kilbas, A., Marichev, O.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, Amsterdam (1993)"},{"issue":"5","key":"22_CR12","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1080\/00207160.2020.1802017","volume":"98","author":"G Usurelu","year":"2021","unstructured":"Usurelu, G., Bejenaru, A., Postolache, M.: Newton-like methods and polynomiographic visualization of modified Thakur process. Int. J. Comput. Math. 98(5), 1049\u20131068 (2021). https:\/\/doi.org\/10.1080\/00207160.2020.1802017","journal-title":"Int. J. Comput. Math."},{"issue":"4","key":"22_CR13","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1137\/1037125","volume":"37","author":"T Ypma","year":"1995","unstructured":"Ypma, T.: Historical development of Newton-Raphson method. SIAM Rev. 37(4), 531\u2013551 (1995). https:\/\/doi.org\/10.1137\/1037125","journal-title":"SIAM Rev."}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2013 ICCS 2022"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-08754-7_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T00:07:32Z","timestamp":1782000452000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-08754-7_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031087530","9783031087547"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-08754-7_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"15 June 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"London","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 June 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 June 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccs-computsci2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iccs-meeting.org\/iccs2022\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"474","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"175","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"78","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"37% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.8","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}