CFD Letters 14, Issue 11 (2022) 1-8 1 CFD Letters Journal homepage: https://semarakilmu.com.my/journals/index.php/CFD_Letters/index ISSN: 2180-1363 Fractional Casson Fluid Flow via Oscillating Motion of Plate and Microchannel Marjan Mohd Daud 1 , Rahimah Mahat 2,* , Lim Yeou Jiann 1 , Sharidan Shafie 1 1 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia 2 Universiti Kuala Lumpur Malaysian Institute of Industrial Technology, Persiaran Sinaran Ilmu, Bandar Seri Alam, 81750, Johor, Malaysia ARTICLE INFO ABSTRACT Article history: Received 5 July 2022 Received in revised form 6 Sept. 2022 Accepted 11 September 2022 Available online 9 November 2022 The impact of the Caputo fractional derivative on the unsteady mixed convention boundary layer flow of Casson fluid is investigated. It is evaluated the flow via two different geometries which are plate and microchannel with oscillating motion. The problems are modelled using a set of partial differential equations with appropriate initial and boundary conditions. The dimensional equations are turned into dimensionless governing equations by using relevant dimensionless variables. The obtained solutions are transformed into fractional form using Caputo fractional derivative. The exact solutions are obtained using the Laplace transform approach. Inverse Laplace transform is applied to the oscillating plate problem while Zakian’s explicit formula approach is used to obtain the results of temperature and velocity profiles. Both profiles are graphed and studied its behaviour in both geometries. The temperature profile is shown to have an opposite pattern of graph for both geometries. While when compared between both geometries on its velocity profile, oscillating plate has a higher velocity compared to oscillating plate. For both profiles, increasing the fractional parameter resulted in a greater pattern. This study aids in the comprehension of Casson fluid flows in fractional systems. Keywords: Oscillating motion; fractional derivative; plate; microchannel 1. Introduction Fractional calculus is used in a wide range of domains, including biology, engineering and economics field. As agreed by other researchers Jan et al., [1] and Qureshi [2] as compared to classical order models, fractional order derivatives are more practical. Since most of real-world problems are subjected to three major mathematical laws. According to Saqib et al., [3] and Abro [4], the laws include the power function, generalized Mittag-Leffler function and exponential decay law. Aside from that, fractional modelling is the sole way to express some of the most important rheological properties of industrialized fluids. Fractional partial differential equations have a variety of distinctive characteristics that make them as a useful mathematical tool for simulating the intricate behaviors of boundary layer flow. The most popular and commonly used fractional derivative operators are Riemann-Liouville and Caputo fractional derivative. However, since Riemann-Liouville fractional * Corresponding author. E-mail address: rahimahm@unikl.edu.my https://doi.org/10.37934/cfdl.14.11.18