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Calculated Shard: 31 (from laksa181)

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curl -X POST \
  'http://laksa031.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.mdpi.com/2504-3110/10/3/171\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.mdpi.com/2504-3110/10/3/171\'))) FORMAT JSONEachRow'

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{"found_url":"https:\/\/www.mdpi.com\/2504-3110\/10\/3\/171","crawl_time":1772654347,"first_indexed_time":0,"http_code":200,"src_unparsed":"com,mdpi!www,\/2504-3110\/10\/3\/171 s443","src_root_hash":"11974975279136771031","history_drop_reason":null,"meta_title":"Sandwich Results for Holomorphic Functions Related to an Integral Operator","meta_descriptions":["In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics."],"attrs_boilerpipe_text":"Search\nfor Articles\n:\nTitle \/ Keyword\nAuthor \/ Affiliation \/ Email\nJournal\nArticle Type\nSection\nSpecial Issue\nVolume\nIssue\nNumber\nPage\nLogical Operator\nOperator\nSearch Text\nSearch Type\nadd_circle_outline\nremove_circle_outline\nArticle Menu\nFont Type:\nArial\nGeorgia\nVerdana\nFont Size:\nAa\nAa\nAa\nLine Spacing:\n\n\n\nColumn Width:\n\n\n\nBackground:\nThis is an early access version, the complete PDF, HTML, and XML versions will be available soon.\nOpen Access\nArticle\nby\nAmal Mohammed Darweesh\n1\n,\nAdel Salim Tayyah\n2\n,\nSarem H. Hadi\n3,*\nand\nAlina Alb Lupaş\n4,*\n1\nDepartment of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf 54001, Iraq\n2\nDepartment of Cybersecurity, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58002, Iraq\n3\nDepartment of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq\n4\nDepartment of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania\n*\nAuthors to whom correspondence should be addressed.\nSubmission received: 6 February 2026\n\/\nRevised: 25 February 2026\n\/\nAccepted: 2 March 2026\n\/\nPublished: 4 March 2026\nAbstract\nIn this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics.\nShare and Cite\nMDPI and ACS Style\nDarweesh, A.M.;                     Tayyah, A.S.;                     Hadi, S.H.;                     Lupaş, A.A.    \n        Sandwich Results for Holomorphic Functions Related to an Integral Operator.\nFractal Fract.\n2026\n,\n10\n, 171.\n    https:\/\/doi.org\/10.3390\/fractalfract10030171\nAMA Style\nDarweesh AM,                                 Tayyah AS,                                 Hadi SH,                                 Lupaş AA.        \n                Sandwich Results for Holomorphic Functions Related to an Integral Operator.\nFractal and Fractional\n. 2026; 10(3):171.\n        https:\/\/doi.org\/10.3390\/fractalfract10030171\nChicago\/Turabian Style\nDarweesh, Amal Mohammed,                                 Adel Salim Tayyah,                                 Sarem H. Hadi,                                 and Alina Alb Lupaş.        \n                2026. \"Sandwich Results for Holomorphic Functions Related to an Integral Operator\"\nFractal and Fractional\n10, no. 3: 171.\n        https:\/\/doi.org\/10.3390\/fractalfract10030171\nAPA Style\nDarweesh, A. M.,                                 Tayyah, A. S.,                                 Hadi, S. H.,                                 & Lupaş, A. A.        \n        \n        (2026). Sandwich Results for Holomorphic Functions Related to an Integral Operator.\nFractal and Fractional\n,\n10\n(3), 171.\n        https:\/\/doi.org\/10.3390\/fractalfract10030171\nArticle Metrics\nArticle metric data becomes available approximately 24 hours after publication online.","attrs_markdown":"Previous Article in Journal \/ Special Issue\n\n[New Certain Results of a Linear Multiplier Fractional *q*\\-Differintegral Operator for Fuzzy Differential Subordination and Superordination](https:\/\/www.mdpi.com\/2504-3110\/10\/3\/170)\n\n## Journals\n[Active Journals](https:\/\/www.mdpi.com\/about\/journals) [Find a Journal](https:\/\/www.mdpi.com\/about\/journalfinder) [Journal Proposal](https:\/\/www.mdpi.com\/about\/journals\/proposal) [Proceedings Series](https:\/\/www.mdpi.com\/about\/proceedings)\n\n[Topics](https:\/\/www.mdpi.com\/topics)\n\n## Information\n[For Authors](https:\/\/www.mdpi.com\/authors) [For Reviewers](https:\/\/www.mdpi.com\/reviewers) [For Editors](https:\/\/www.mdpi.com\/editors) [For Librarians](https:\/\/www.mdpi.com\/librarians) [For Publishers](https:\/\/www.mdpi.com\/publishing_services) [For Societies](https:\/\/www.mdpi.com\/societies) [For Conference Organizers](https:\/\/www.mdpi.com\/conference_organizers)\n\n[Open Access Policy](https:\/\/www.mdpi.com\/openaccess) [Institutional Open Access Program](https:\/\/www.mdpi.com\/ioap) [Special Issues Guidelines](https:\/\/www.mdpi.com\/special_issues_guidelines) [Editorial Process](https:\/\/www.mdpi.com\/editorial_process) [Research and Publication Ethics](https:\/\/www.mdpi.com\/ethics) [Article Processing Charges](https:\/\/www.mdpi.com\/apc) [Awards](https:\/\/www.mdpi.com\/awards) [Testimonials](https:\/\/www.mdpi.com\/testimonials)\n\n[Author Services](https:\/\/www.mdpi.com\/authors\/english)\n\n## Initiatives\n[Sciforum](https:\/\/sciforum.net\/) [MDPI Books](https:\/\/www.mdpi.com\/books) [Preprints.org](https:\/\/www.preprints.org\/) [Scilit](https:\/\/www.scilit.com\/) [SciProfiles](https:\/\/sciprofiles.com\/) [Encyclopedia](https:\/\/encyclopedia.pub\/) [JAMS](https:\/\/jams.pub\/) [Proceedings Series](https:\/\/www.mdpi.com\/about\/proceedings)\n\n## About\n[Overview](https:\/\/www.mdpi.com\/about) [Contact](https:\/\/www.mdpi.com\/about\/contact) [Careers](https:\/\/careers.mdpi.com\/) [News](https:\/\/www.mdpi.com\/about\/announcements) [Press](https:\/\/www.mdpi.com\/about\/press) [Blog](http:\/\/blog.mdpi.com\/)\n\n[Sign In \/ Sign Up](https:\/\/www.mdpi.com\/user\/login)\n\n## Notice\n[*clear*]()\n\n## Notice\nYou are accessing a machine-readable page. 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Alb](http:\/\/www.pubmed.gov\/?cmd=Search&term=Alina%20Alb%20Lupa%C5%9F)\n\n- [Table of Contents](https:\/\/www.mdpi.com\/2504-3110\/10\/3\/171#table_of_contents)\n\nAltmetric   [*share* Share](https:\/\/www.mdpi.com\/2504-3110\/10\/3\/171 \"Share\")   [*announcement* Help](https:\/\/www.mdpi.com\/2504-3110\/10\/3\/171 \"Help\")   [*format\\_quote* Cite]()   [*question\\_answer* Discuss in SciProfiles](https:\/\/sciprofiles.com\/discussion-groups\/public\/10.3390\/fractalfract10030171?utm_source=mpdi.com&utm_medium=publication&utm_campaign=discuss_in_sciprofiles \"Discuss in Sciprofiles\")\n\n## Need Help?\n### Support\nFind support for a specific problem in the support section of our website.\n\n[Get Support](https:\/\/www.mdpi.com\/about\/contactform)\n\n### Feedback\nPlease let us know what you think of our products and services.\n\n[Give Feedback](https:\/\/www.mdpi.com\/feedback\/send)\n\n### Information\nVisit our dedicated information section to learn more about MDPI.\n\n[Get Information](https:\/\/www.mdpi.com\/authors)\n\n[*clear*]()\n\n## JSmol Viewer\n[*clear*]()\n\n*first\\_page*\n\n[Download PDF](https:\/\/www.mdpi.com\/2504-3110\/10\/3\/171\/pdf?version=1772640263)\n\n*settings*\n\n[Order Article Reprints](https:\/\/www.mdpi.com\/2504-3110\/10\/3\/171\/reprints)\n\nFont Type:\n\n*Arial* *Georgia* *Verdana*\n\nFont Size:\n\nAa Aa Aa\n\nLine Spacing:\n\n**   **   **\n\nColumn Width:\n\n**   **   **\n\nBackground:\n\n**This is an early access version, the complete PDF, HTML, and XML versions will be available soon.**\n\nOpen AccessArticle\n\n# Sandwich Results for Holomorphic Functions Related to an Integral Operator\nby\n\nAmal Mohammed Darweesh\n\n![](https:\/\/www.mdpi.com\/bundles\/mdpisciprofileslink\/img\/unknown-user.png)Amal Mohammed Darweesh\n\n[SciProfiles](https:\/\/sciprofiles.com\/profile\/1939060?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name)  [Scilit](https:\/\/scilit.com\/scholars?q=Amal%20Mohammed%20Darweesh)  [Preprints.org](https:\/\/www.preprints.org\/search?condition_blocks=[{%22value%22:%22Amal+Mohammed+Darweesh%22,%22type%22:%22author%22,%22operator%22:null}]&sort_field=relevance&sort_dir=desc&page=1&exact_match=true)  [Google Scholar](https:\/\/scholar.google.com\/scholar?q=Amal+Mohammed+Darweesh)\n\n1,\n\nAdel Salim Tayyah\n\n![](https:\/\/www.mdpi.com\/profiles\/3391242\/thumb\/Adel_Salim_Tayyah.jpg)Adel Salim Tayyah\n\n[SciProfiles](https:\/\/sciprofiles.com\/profile\/3391242?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name)  [Scilit](https:\/\/scilit.com\/scholars?q=Adel%20Salim%20Tayyah)  [Preprints.org](https:\/\/www.preprints.org\/search?condition_blocks=[{%22value%22:%22Adel+Salim+Tayyah%22,%22type%22:%22author%22,%22operator%22:null}]&sort_field=relevance&sort_dir=desc&page=1&exact_match=true)  [Google Scholar](https:\/\/scholar.google.com\/scholar?q=Adel+Salim+Tayyah)\n\n2[![](https:\/\/pub.mdpi-res.com\/img\/design\/orcid.png?0465bc3812adeb52?1772608368)](https:\/\/orcid.org\/0000-0002-4380-1428),\n\nSarem H. Hadi\n\n![](https:\/\/www.mdpi.com\/profiles\/1001008\/thumb\/Sarem_H._Hadi.jpg)Sarem H. 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The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics.\n\n**Keywords:**  holomorphic functions; logarithmic integral operator; fractional calculus; differential subordination; sandwich-type results  [holomorphic functions](https:\/\/www.mdpi.com\/search?q=holomorphic%20functions); [logarithmic integral operator](https:\/\/www.mdpi.com\/search?q=logarithmic%20integral%20operator); [fractional calculus](https:\/\/www.mdpi.com\/search?q=fractional%20calculus); [differential subordination](https:\/\/www.mdpi.com\/search?q=differential%20subordination); [sandwich-type results](https:\/\/www.mdpi.com\/search?q=sandwich-type%20results)\n\n## Share and Cite\n**MDPI and ACS Style**\n\nDarweesh, A.M.; Tayyah, A.S.; Hadi, S.H.; Lupaş, A.A. Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal Fract.* **2026**, *10*, 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**AMA Style**\n\nDarweesh AM, Tayyah AS, Hadi SH, Lupaş AA. Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal and Fractional*. 2026; 10(3):171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**Chicago\/Turabian Style**\n\nDarweesh, Amal Mohammed, Adel Salim Tayyah, Sarem H. Hadi, and Alina Alb Lupaş. 2026. \"Sandwich Results for Holomorphic Functions Related to an Integral Operator\" *Fractal and Fractional* 10, no. 3: 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**APA Style**\n\nDarweesh, A. M., Tayyah, A. S., Hadi, S. H., & Lupaş, A. A. (2026). Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal and Fractional*, *10*(3), 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n## Article Metrics\nNo\n\nNo\n\nArticle metric data becomes available approximately 24 hours after publication online.\n\n[Zoom]() \\|  [Orient]()  \\|  [As Lines]()  \\|  [As Sticks]()  \\|  [As Cartoon]()  \\|  [As Surface]()  \\| [Previous Scene]() \\| [Next Scene]()\n\n## Cite\nExport citation file: [BibTeX]() \\| [EndNote]() \\| [RIS]()\n\n**MDPI and ACS Style**\n\nDarweesh, A.M.; Tayyah, A.S.; Hadi, S.H.; Lupaş, A.A. Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal Fract.* **2026**, *10*, 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**AMA Style**\n\nDarweesh AM, Tayyah AS, Hadi SH, Lupaş AA. Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal and Fractional*. 2026; 10(3):171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**Chicago\/Turabian Style**\n\nDarweesh, Amal Mohammed, Adel Salim Tayyah, Sarem H. Hadi, and Alina Alb Lupaş. 2026. \"Sandwich Results for Holomorphic Functions Related to an Integral Operator\" *Fractal and Fractional* 10, no. 3: 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**APA Style**\n\nDarweesh, A. M., Tayyah, A. S., Hadi, S. H., & Lupaş, A. A. (2026). 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Hadi 3,\\*[![](https:\/\/pub.mdpi-res.com\/img\/design\/orcid.png?0465bc3812adeb52?1772608368)](https:\/\/orcid.org\/0000-0002-3780-2360) andAlina Alb Lupaş 4,\\*[![](https:\/\/pub.mdpi-res.com\/img\/design\/orcid.png?0465bc3812adeb52?1772608368)](https:\/\/orcid.org\/0000-0002-2855-7535)\n\n1\n\nDepartment of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf 54001, Iraq\n\n2\n\nDepartment of Cybersecurity, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58002, Iraq\n\n3\n\nDepartment of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq\n\n4\n\nDepartment of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania\n\n\\*\n\nAuthors to whom correspondence should be addressed.\n\nSubmission received: 6 February 2026 \/ Revised: 25 February 2026 \/ Accepted: 2 March 2026 \/ Published: 4 March 2026\n\n## Abstract\nIn this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics.\n\n## Share and Cite\n**MDPI and ACS Style**\n\nDarweesh, A.M.; Tayyah, A.S.; Hadi, S.H.; Lupaş, A.A. Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal Fract.* **2026**, *10*, 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**AMA Style**\n\nDarweesh AM, Tayyah AS, Hadi SH, Lupaş AA. Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal and Fractional*. 2026; 10(3):171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**Chicago\/Turabian Style**\n\nDarweesh, Amal Mohammed, Adel Salim Tayyah, Sarem H. Hadi, and Alina Alb Lupaş. 2026. \"Sandwich Results for Holomorphic Functions Related to an Integral Operator\" *Fractal and Fractional* 10, no. 3: 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n\n**APA Style**\n\nDarweesh, A. M., Tayyah, A. S., Hadi, S. H., & Lupaş, A. A. (2026). Sandwich Results for Holomorphic Functions Related to an Integral Operator. *Fractal and Fractional*, *10*(3), 171. https:\/\/doi.org\/10.3390\/fractalfract10030171\n## Article Metrics\nArticle metric data becomes available approximately 24 hours after publication online.","meta_canonical":null}

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Meta Title	Sandwich Results for Holomorphic Functions Related to an Integral Operator
Meta Description	In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics.
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Boilerpipe Text	Search for Articles : Title / Keyword Author / Affiliation / Email Journal Article Type Section Special Issue Volume Issue Number Page Logical Operator Operator Search Text Search Type add_circle_outline remove_circle_outline Article Menu Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: This is an early access version, the complete PDF, HTML, and XML versions will be available soon. Open Access Article by Amal Mohammed Darweesh 1 , Adel Salim Tayyah 2 , Sarem H. Hadi 3,* and Alina Alb Lupaş 4,* 1 Department of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf 54001, Iraq 2 Department of Cybersecurity, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58002, Iraq 3 Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq 4 Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania * Authors to whom correspondence should be addressed. Submission received: 6 February 2026 / Revised: 25 February 2026 / Accepted: 2 March 2026 / Published: 4 March 2026 Abstract In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics. Share and Cite MDPI and ACS Style Darweesh, A.M.; Tayyah, A.S.; Hadi, S.H.; Lupaş, A.A. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal Fract. 2026 , 10 , 171. https://doi.org/10.3390/fractalfract10030171 AMA Style Darweesh AM, Tayyah AS, Hadi SH, Lupaş AA. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal and Fractional . 2026; 10(3):171. https://doi.org/10.3390/fractalfract10030171 Chicago/Turabian Style Darweesh, Amal Mohammed, Adel Salim Tayyah, Sarem H. Hadi, and Alina Alb Lupaş. 2026. "Sandwich Results for Holomorphic Functions Related to an Integral Operator" Fractal and Fractional 10, no. 3: 171. https://doi.org/10.3390/fractalfract10030171 APA Style Darweesh, A. M., Tayyah, A. S., Hadi, S. H., & Lupaş, A. A. (2026). Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal and Fractional , 10 (3), 171. https://doi.org/10.3390/fractalfract10030171 Article Metrics Article metric data becomes available approximately 24 hours after publication online.
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Open AccessArticle # Sandwich Results for Holomorphic Functions Related to an Integral Operator by Amal Mohammed Darweesh ![](https://www.mdpi.com/bundles/mdpisciprofileslink/img/unknown-user.png)Amal Mohammed Darweesh [SciProfiles](https://sciprofiles.com/profile/1939060?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name) [Scilit](https://scilit.com/scholars?q=Amal%20Mohammed%20Darweesh) [Preprints.org](https://www.preprints.org/search?condition_blocks=[{%22value%22:%22Amal+Mohammed+Darweesh%22,%22type%22:%22author%22,%22operator%22:null}]&sort_field=relevance&sort_dir=desc&page=1&exact_match=true) [Google Scholar](https://scholar.google.com/scholar?q=Amal+Mohammed+Darweesh) 1, Adel Salim Tayyah ![](https://www.mdpi.com/profiles/3391242/thumb/Adel_Salim_Tayyah.jpg)Adel Salim Tayyah [SciProfiles](https://sciprofiles.com/profile/3391242?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name) [Scilit](https://scilit.com/scholars?q=Adel%20Salim%20Tayyah) [Preprints.org](https://www.preprints.org/search?condition_blocks=[{%22value%22:%22Adel+Salim+Tayyah%22,%22type%22:%22author%22,%22operator%22:null}]&sort_field=relevance&sort_dir=desc&page=1&exact_match=true) [Google Scholar](https://scholar.google.com/scholar?q=Adel+Salim+Tayyah) 2[![](https://pub.mdpi-res.com/img/design/orcid.png?0465bc3812adeb52?1772608368)](https://orcid.org/0000-0002-4380-1428), Sarem H. 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Fractal Fract. 2026, 10(3), 171; <https://doi.org/10.3390/fractalfract10030171> Submission received: 6 February 2026 / Revised: 25 February 2026 / Accepted: 2 March 2026 / Published: 4 March 2026 (This article belongs to the Special Issue [Fractional Calculus, Quantum Calculus and Special Functions in Complex Analysis](https://www.mdpi.com/2504-3110/10/3/%20%20%20%20%20%20%20%20%0A%20%20%20%20/journal/fractalfract/special_issues/F2082M84PQ%0A)) [Download keyboard\_arrow\_down]() [Download PDF](https://www.mdpi.com/2504-3110/10/3/171/pdf?version=1772640263) [Versions Notes](https://www.mdpi.com/2504-3110/10/3/171/notes) ## Abstract In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics. Keywords: holomorphic functions; logarithmic integral operator; fractional calculus; differential subordination; sandwich-type results [holomorphic functions](https://www.mdpi.com/search?q=holomorphic%20functions); [logarithmic integral operator](https://www.mdpi.com/search?q=logarithmic%20integral%20operator); [fractional calculus](https://www.mdpi.com/search?q=fractional%20calculus); [differential subordination](https://www.mdpi.com/search?q=differential%20subordination); [sandwich-type results](https://www.mdpi.com/search?q=sandwich-type%20results) ## Share and Cite MDPI and ACS Style Darweesh, A.M.; Tayyah, A.S.; Hadi, S.H.; Lupaş, A.A. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal Fract. 2026, 10, 171. https://doi.org/10.3390/fractalfract10030171 AMA Style Darweesh AM, Tayyah AS, Hadi SH, Lupaş AA. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal and Fractional. 2026; 10(3):171. https://doi.org/10.3390/fractalfract10030171 Chicago/Turabian Style Darweesh, Amal Mohammed, Adel Salim Tayyah, Sarem H. Hadi, and Alina Alb Lupaş. 2026. "Sandwich Results for Holomorphic Functions Related to an Integral Operator" Fractal and Fractional 10, no. 3: 171. https://doi.org/10.3390/fractalfract10030171 APA Style Darweesh, A. M., Tayyah, A. S., Hadi, S. H., & Lupaş, A. A. (2026). Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal and Fractional, 10(3), 171. https://doi.org/10.3390/fractalfract10030171 ## Article Metrics No No Article metric data becomes available approximately 24 hours after publication online. [Zoom]() \\| [Orient]() \\| [As Lines]() \\| [As Sticks]() \\| [As Cartoon]() \\| [As Surface]() \\| [Previous Scene]() \\| [Next Scene]() ## Cite Export citation file: [BibTeX]() \\| [EndNote]() \\| [RIS]() MDPI and ACS Style Darweesh, A.M.; Tayyah, A.S.; Hadi, S.H.; Lupaş, A.A. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal Fract. 2026, 10, 171. https://doi.org/10.3390/fractalfract10030171 AMA Style Darweesh AM, Tayyah AS, Hadi SH, Lupaş AA. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal and Fractional. 2026; 10(3):171. https://doi.org/10.3390/fractalfract10030171 Chicago/Turabian Style Darweesh, Amal Mohammed, Adel Salim Tayyah, Sarem H. Hadi, and Alina Alb Lupaş. 2026. "Sandwich Results for Holomorphic Functions Related to an Integral Operator" Fractal and Fractional 10, no. 3: 171. https://doi.org/10.3390/fractalfract10030171 APA Style Darweesh, A. M., Tayyah, A. S., Hadi, S. H., & Lupaş, A. A. (2026). Sandwich Results for Holomorphic Functions Related to an Integral Operator. 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Readable Markdown	[![fractalfract-logo](https://pub.mdpi-res.com/img/journals/fractalfract-logo.png?8f9eae8e215192f5)](https://www.mdpi.com/journal/fractalfract) Article Menu Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: This is an early access version, the complete PDF, HTML, and XML versions will be available soon. Open AccessArticle by Amal Mohammed Darweesh 1,Adel Salim Tayyah 2[![](https://pub.mdpi-res.com/img/design/orcid.png?0465bc3812adeb52?1772608368)](https://orcid.org/0000-0002-4380-1428),Sarem H. Hadi 3,\[![](https://pub.mdpi-res.com/img/design/orcid.png?0465bc3812adeb52?1772608368)](https://orcid.org/0000-0002-3780-2360) andAlina Alb Lupaş 4,\[![](https://pub.mdpi-res.com/img/design/orcid.png?0465bc3812adeb52?1772608368)](https://orcid.org/0000-0002-2855-7535) 1 Department of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf 54001, Iraq 2 Department of Cybersecurity, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58002, Iraq 3 Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq 4 Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania \* Authors to whom correspondence should be addressed. Submission received: 6 February 2026 / Revised: 25 February 2026 / Accepted: 2 March 2026 / Published: 4 March 2026 ## Abstract In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics. ## Share and Cite MDPI and ACS Style Darweesh, A.M.; Tayyah, A.S.; Hadi, S.H.; Lupaş, A.A. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal Fract. 2026, 10, 171. https://doi.org/10.3390/fractalfract10030171 AMA Style Darweesh AM, Tayyah AS, Hadi SH, Lupaş AA. Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal and Fractional. 2026; 10(3):171. https://doi.org/10.3390/fractalfract10030171 Chicago/Turabian Style Darweesh, Amal Mohammed, Adel Salim Tayyah, Sarem H. Hadi, and Alina Alb Lupaş. 2026. "Sandwich Results for Holomorphic Functions Related to an Integral Operator" Fractal and Fractional 10, no. 3: 171. https://doi.org/10.3390/fractalfract10030171 APA Style Darweesh, A. M., Tayyah, A. S., Hadi, S. H., & Lupaş, A. A. (2026). Sandwich Results for Holomorphic Functions Related to an Integral Operator. Fractal and Fractional, 10(3), 171. https://doi.org/10.3390/fractalfract10030171 ## Article Metrics Article metric data becomes available approximately 24 hours after publication online.
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