### Analysing MHD Heat-Mass Transfer model for-Oldroyd-B Fluid Using Fractional Order Prabhakar Derivative

**Azhar Ali Zafar, Sajjad Hussain, Khurram Shabbir**

**Abstract:**The manuscript explores a fractional order heat-mass transfer model for Oldroyd-B fluid on a vertical plate employing the Prabhakar derivative operator. It investigates the MHD flow of Oldroyd-B fluid induced by natural convection and the general motion of the plate. Well known integral transform i.e. Laplace transform and Tzou’s numerical inversion algorithm are employed to simulate the model under generalized constraints. Several scenarios involving the generalized motion of the plate and general boundary conditions are investigated. A comprehensive graphical analysis is conducted to investigate the control of system parameters, and valuable findings are concluded that can help to optimize and foster various processes.