Hybrid nanofluids (HNFs) comprise combinations of different nanoparticles suspended in base fluids. Applications of such nanofluids are growing in the areas of energy and biomedical engineering including smart (functional) coatings. Motivated by these developments, the present article examines theoretically the magnetohydrodynamic (MHD) coating boundary layer flow of HNFs from a stretching surface under a transverse magnetic field in porous media with chemically reactive nanoparticles. Darcy’s law is deployed. Both first and second order momentum slip is included as is solutal slip. The transformed boundary value problem is solved analytically. Closed form solutions for velocity are derived in terms of exponential functions and for the concentration field in terms of incomplete Gamma functions by the application of the Laplace transformation technique.The influence of selected parameters e.g. suction/injection, magnetic field and slip parameterson velocity and concentration distributions are visualized graphically. Concentration magnitudes are elevated with stronger magnetic field whereas they are suppressed with greater wall solutal slip. Magnetic field suppresses velocity and increases hydrodynamic boundary layer thickness. The flow is accelerated with reduction in inverse Darcy number and stronger suction leads to a decrease in skin friction. The analysis provides a good foundation for further investigations using numerical methods.

This research paper discusses the analytical and semi-analytical solutions of the quadratic–cubic fractional nonlinear Schrodinger (NLS) equation. By applying a new fractional operator we transform the fractional formula of the model to integer-order, which allows applying the analytical and numerical methods on it. The analytical solutions are obtained by the implementation of two distinct systematic schemes and the reported solutions are used in applying the Adomian decomposition method to get the semi-analytical wave solutions of this model. These solutions are used to characterize the changes over time of a physical system in which case of quantum influence, such as wave-particle duality. The comparison between the analytical and semi-analytical solutions are given to explain the accuracy of the obtained solutions.

In the current research work, we are going to discuss the Modified Bergman's Minimal blood glucose-insulin model.We are restructuring the old model by including one more component known as diet, which is also very essential for blood glucose model. Many years ago the minimal model was define which explain the relation between blood glucose and insulin level, and after that a lots of work and research has been done on it. We define the fractional model to show the strength of Caputo-Fabrizio fractional derivative and also examined the existence and uniqueness of the result along with its numerical and graphical representation.