University of Tehran Press Journal of Computational Applied Mechanics 2423-6713 56 2 2025 04 01 Exact solutions for Two-dimensional flow of Fractional NTNN fluid within an oscillatory rectangular enclosure 457 469 102104 10.22059/jcamech.2025.390562.1370 EN Sohail Nadeem Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan Department of Mathematics and Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia Department of Mathematics, Wenzhou University, Wenzhou, 325035, China 0000-0002-1052-011X Sobia Naz Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan Bushra Ishtiaq Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan Jehad Alzabut Department of Mathematics and Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia Department of Industrial Engineering, OSTIM Technical University, Ankara 06374, Türkiye Journal Article 2025 02 15 In this paper, we present an analysis for the unsteady two-dimensional flow of incompressible fractional NTNN model. The purpose of this research is to detect exact solutions for the cosine oscillation inside an oscillating rectangular duct having fractional fluid. The mixed initial-boundary value problem is simplified by using Laplace and double finite Fourier sine transform. The impacts of pertinent parameters on the velocity profile and the corresponding shear stresses are analyzed through graphical illustrations for cosine oscillation. Our results indicate that the fluid's flow rises in correlation with fractional and rheological factors, such as α,N,ω, and t. As limiting cases of exact solution, the results can also be obtained for the ordinary NTNN and Newtonian fluid. https://jcamech.ut.ac.ir/article_102104_eb366f8316434f9da41994bb655a079f.pdf