Muhammad Bilal Riaz - Department of Mathematics, University of Management and Technology, Lahore, ۵۴۰۰۰, Pakistan
Syed Tauseef Saeed - Department of Science & Humanities, National University of Computer and Emerging Sciences, Lahore Campus, ۵۴۰۰۰, Pakistan‎
Dumitru Baleanu - Department of Mathematics, Cankaya University, Ankara, ۰۶۷۹۰, Turkey

The dynamical analysis of MHD second grade fluid based on their physical properties has stronger resistance capabilities, low-frequency responses, lower energy consumption, and higher sensitivities; due to these facts externally applied magnetic field always takes the forms of diamagnetic, ferromagnetic and paramagnetic. The mathematical modeling based on the fractional treatment of governing equation subject to the temperature distribution, concentration, and velocity field is developed within a porous surfaced plate.  Fractional differential operators with and without non-locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. The fractionalized analytical solutions have been traced out separately through Atangana-Baleanu and Caputo-Fabrizio fractional differential operators. Our results suggest that the velocity profile decrease by increasing the value of the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.

Second grade fluid, Fractional differential operator, Magnetic field, Chemical reaction, non-Singular kernels