International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3248 2020 2020 On A Subclass of Analytic Functions Specified By Touchard Polynomials Mathematics Education Program, Faculty of Education and Arts, Sohar University,Sohar 3111, Oman Ala Ala Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13132, Jordan 𝐎πͺπ₯𝐚𝐑 𝐀π₯ π‘πžπŸπšπ’ π‘πžπŸπšπ’ 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’πͺ 𝐀π₯ π‡πšπ°πšπ«π² π‡πšπ°πšπ«π² College of Applied and Health Sciences, A'Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman π‰πšπ¦πšπ₯ π’πšπ₯𝐚𝐑 π’πšπ₯𝐚𝐑 Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan 𝐁𝐚𝐬𝐞𝐦 π…π«πšπ¬π’π§ π…π«πšπ¬π’π§ 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 2025 123 131 10.54216/IJNS.250312 https://www.americaspg.com/articleinfo/21/show/3248