Time fractional Yang–Abdel–Cattani derivative in generalized MHD Casson fluid flow with heat source and chemical reaction

Abstract

AbstractThis present research article investigates the exact analytical solution for the mathematical model of the generalized Casson fluid flow by using the new fractional operator with Rabotnov exponential kernel i.e. Yang–Abdel–Cattani operator. The impacts of heat source, magnetic hydrodynamics and chemical reactions on the flow of fractional Casson fluid through a vertical flat plate are studied in this article. For the sake of a better interpretation of the rheological behavior of Casson fluid we have used the new operator of fractional order with exponential kernel of Rabotnov known as Yang–Abdel–Cattani operator of fractional derivative. By making use of the technique of Laplace transform we have find the exact analytical solution of the problem in the Mittag–Leffler’s form, for all the three governing equations i.e. Velocity, energy and concentration equation. It has been noticed from the literature that it is challenging to obtain analytical results from fractional fluid model derived by the various fractional operators. This article helps to address this issue by providing analytical solutions for fractionalized fluid models. To analyze the physical importance of different fluid parameters such as Schmidt number, Prandtl number, MHD and alpha on the heat, mass and momentum class are presented through graphs. The concentration of the fluid decreases with Schmidth number and temperature of the fluid decreases with the increasing Prandtl number. The velocity of the fluid decreases with increasing MHD effects and increases with increasing Alpha. The Yang–Abdel–Cattani operator of fractional order can describe the memory effects more suitably than the other fractional operators.