Free convection MHD flow of viscous fluid by means of damped shear and thermal flux in a vertical circular tube

The main concern of the article is to study the hydromagnetic, free convection, and incompressible viscous fluid flow with generalized boundary conditions. The movement of the fluid is taken into account through a vertical circular tube. We built up a fractional model with the assistance of the constitutive shear stress equation and generalized type of Fourier's Law. We've received closed-form solutions of the dimensionless fractional model by the way of Laplace and finite Hankel transform approach and received results are stated relating the G-function of Lorenzo and Hartley and in the generalized form of Mittag-Leffler. Graphically, the impacts of a choice of fractional and material variables are plotted by the use of Mathcad. The velocity is expanded by expanding the values of fractional factors alpha and beta. The boundary layer difference increment as time is expanded. The boundary layer difference and velocity are expanding by decreasing the value of the magnetic field.