aspg-21-3248-1791472118 20261008150838 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 3 On A Subclass of Analytic Functions Specified By Touchard Polynomials Ala Amourah Mathematics Education Program, Faculty of Education and Arts, Sohar University,Sohar 3111, Oman 𝐎πͺπ₯𝐚𝐑 𝐀π₯ π‘πžπŸπšπ’ Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13132, Jordan π“πšπ«π’πͺ 𝐀π₯ π‡πšπ°πšπ«π² Department of Applied Science, Ajloun College, Al balqa Applied University, Ajloun 26816. Jordan; Jadara Research Center, Jadara University, Irbid 21110, Jordan π‰πšπ¦πšπ₯ π’πšπ₯𝐚𝐑 College of Applied and Health Sciences, A'Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman 𝐁𝐚𝐬𝐞𝐦 π…π«πšπ¬π’π§ Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan In this investigation, we present a new collection of analytic functions that includes Touchard polynomials. We then aim to calculate the Maclaurin coefficients |π‘Ž2 | and |π‘Ž3 | and address the Fekete-SzegΓΆ functional problem within this specific subfamily. Additionally, we demonstrate several new outcomes by specifying the parameters used in our main findings. 2025 123 131 3248 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250312 https://www.americaspg.com/journal/21/article/3248 https://www.americaspg.com/storage/61737029302.pdf