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Abstract Fractional MHD viscoelastic fluid flow has been discussed in this study. Two dimensional and two directional unsteady flow field is more critically analyzed via non-integer time derivatives. Three memory parameters are incorporated to explore the viscoelastic characteristics of the model. Variations in concentration occurred due to homogeneous-heterogeneous reactions in the flow domain. Change in concentrations consequently leads to one of the lasting chemical species. Heterogeneous reactions are observed at the boundary while homogeneous reactions are seen in the flowing region. We consider different orders of diffusion coefficients of chemical reacting species to tackle the wider class of physical and chemical processes. Governing equations are nonlinear in nature. Hence a recently established finite difference technique along with " L 1 algorithm" is used for discretization and solution of governing fractional partial differential equations. Presence of chemical reactions in flow process made the simulations valuable for chemical industry. Highlights • Unsteady two dimensional fractional flow is constructed. • Chemical species are considered with unequal diffusivities. • Average Sherwood numbers are plotted for pertinent parameters. • Finite difference algorithm is used for solution of governing equations. [ABSTRACT FROM AUTHOR]

The current article numerically investigates the time-dependent fractional non-Newtonian fluid model on a vertical plane in a Darcy medium. A generalized Scott-Bliar model with heterogeneous and homogeneous interaction is employed to control the flow and mass transfer in the boundary layer region. Chemical reactions in flow are responsible for variable concentration, which causes long-lasting chemical species to better understand the chemical process.The highly nonlinear coupled model is discretized using the finite difference method with the L 1 technique. The current analysis shows that the fractional exponent significantly affects the concentration of chemical species. It also revealed during the studies that for maximum values of K r and δ 1 the concentration of chemical species for a reduces. Currently no such result in the literary works for the non-integer fractional Casson model. This analysis is help full to understand the chemical process in fractional Casson fluid model. [ABSTRACT FROM AUTHOR]

• Non-integer derivatives are explored for unequal diffusivity of chemical spices Forchheimer Medium. • Theoretical Error and convergence analysis are carried out. • The Finite Difference method is constructed along with the L1 algorithm. • Average mass transfer rates are analyzed through plots for different physical parameters. Owing to the fact that fractional viscoelastic models contribute significantly with application point of view, a good number of researchers have diverted their attention to this area. In the current study, we have carried out a numerical investigation of the fractional viscoelastic fluid model with unsteady convection, on an inclined plane, via Forchheimer medium. Furthermore, we have presented the generalized Scott-Bliar model to Caput-type fractional derivatives with homogeneous-heterogeneous reactions in the constitutive relations. The viscoelastic features of the proposed model are explored by introducing three memory parameters. The homogeneous-heterogeneous reactions in the flow domain cause variations in the concentration, leading to one of the long-lasting chemical species. One can witness the homogeneous reactions in the flowing region, whereas the heterogeneous reactions occur at the boundary. A broader cluster of physical and chemical processes is tackled by considering diffusion coefficients of a different order. The well-known finite difference technique combined with the " L 1 algorithm" is utilized to discretize the principal nonlinear boundary layer equations. The proposed numerical scheme is being validated by performing error and convergence analysis so that a thorough investigation of the chemical reaction process through the Forchheimer medium in the viscoelastic fluid model may be carried out. The proposed mathematical approach may be regarded as a valuable technique for studying the viscoelastic model and chemical reaction processes in a fluid to formulate schemes dealing with unsteady convection. Resultantly, this model can be utilized in the chemical industry. [ABSTRACT FROM AUTHOR]