Volume 20 (2024) Issue 2

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.

Abstract: A Monad graph is a graph Γ in which each of its vertices belongs to a finite group G and connects with its image under the action of a linear map f. This kind of graph was introduced by V. Arnold in 2003. In this paper, we compute the Monad graphs in which G is isomorphic to a cyclic group C_n of order n and f the fifth power function, i.e. f(g) = g⁵. Furthermore, some algebraic and dynamical properties of the studied Monad graphs are obtained. The proofs of our results are based on various tools and results with regard to the fields of number theory, algebra and graph theory.