Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 93, Issue 1 (2022) 50-63 50 Journal of Advanced Research in Fluid Mechanics and Thermal Sciences Journal homepage: https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/index ISSN: 2811-3950 Application of Caputo Fractional Derivatives to the Convective Flow of Casson Fluids in a Microchannel with Thermal Radiation Marjan Mohd Daud 1 , Lim Yeou Jiann 1 , Rahimah Mahat 2 , Sharidan Shafie 1,* 1 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia 2 Universiti Kuala Lumpur Malaysian Institute of Industrial Technology, Persiaran Sinaran Ilmu, Bandar Seri Alam, 81750 Johor Bahru, Malaysia ARTICLE INFO ABSTRACT Article history: Received 17 July 2021 Received in revised form 8 January 2022 Accepted 9 January 2022 Available online 3 March 2022 In this paper, the application of Caputo fractional derivative on unsteady boundary layer Casson fluid flow in a microchannel is studied. The partial differential equations which governed the problem are considered with the presence of thermal radiation. The fractional partial differential equations are transformed into dimensionless governing equations using appropriate dimensionless variables. It is then solved analytically using the Laplace transform technique which transforms the equations into linear ordinary differential equations. These transformed equations are then solved using the appropriate method, and the inverse Laplace transform technique is applied to obtain the solution in form of velocity and temperature profiles. Graphical illustrations are acquired using Mathcad software and the influence of important physical parameters on velocity and temperature profiles are analyzed. Results show that thermal radiation and fractional parameter have enhanced the velocity and temperature profiles. Keywords: Caputo fractional derivative; thermal radiation; Laplace transform 1. Introduction Generally, most of the motion in nature such as fluid flow, heat transfer, the wave of sound, and others can be mathematically described by using the partial differential equation (PDE). Natural phenomena including velocity and acceleration are normally described in derivatives [1]. Besides, PDEs are often used by scientists and engineers to explore a wide range of physical phenomena including fluid dynamics, electricity, and thermal transfer. In 2007, Jumarie [2] has investigated PDE using fractional derivative and solve using modified Riemann-Liouville derivative. Based on Khalil et al., [3], the fractional derivative has been existed a long time ago, even as old as calculus. The application of fractional derivatives has provided more general and accurate models of a system compared to the traditional calculus since it is concerned with the real or complex order generalization of integrals and derivatives. Due to order differentiation features, systems described with fractional calculus are non-linear and may exhibit a significantly richer dynamical behavior. Moreover, the most real-world problem is modeled by a * Corresponding author. E-mail address: sharidan@utm.my https://doi.org/10.37934/arfmts.93.1.5063