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It is fundamental fact that nanoparticles are strong function of their shapes and sizes; this is because nanoparticles certainly play an adhesive and a significant role in fluid phenomenon. This manuscript investigates the functionality and thermodynamics of different nanoparticles namely gold, alumina, silver and copper suspended in ethylene glycol considered as a base fluid. The problem of mixed convection is modeled by modern fractional derivative by invoking initial and boundary conditions. The analytic calculation of velocity field and temperature distribution is obtained by employing Laplace transforms then transformed into Fox-H function. The effects of critical physical characteristics (sizes and shapes) have been analyzed through velocity field and temperature distribution using different nanoparticles. Obviously, all nanoparticles are not made equal in terms of sizes and shapes; hence a remarkable comparison of different nanoparticles is analyzed for the interactions with their sizes and shapes on the velocity field and temperature distribution. Importantly, we seek to illustrate the shape and size impacts of nanoparticles namely platelet, blade, cylinder and brick on velocity field and temperature distribution. In short, our results suggest that E G − A u moves more rapidly in comparison with E G − A l 2 0 3 , E G − A g and E G − C u at larger time while E G − C u moves faster in comparison with E G − A l 2 0 3 , E G − A g and E G − A u for smaller time. The identical similarities and differences have also been analyzed on the basis of shape and size impacts of nanoparticles.

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This investigative study is focused on the impact of wavelet on traditional forecasting time-series models, which significantly shows the usage of wavelet algorithms. Wavelet Decomposition (WD) algorithm has been combined with various traditional forecasting time-series models, such as Least Square Support Vector Machine (LSSVM), Artificial Neural Network (ANN) and Multivariate Adaptive Regression Splines (MARS) and their effects are examined in terms of the statistical estimations. The WD has been used as a mathematical application in traditional forecast modelling to collect periodically measured parameters, which has yielded tremendous constructive outcomes. Further, it is observed that the wavelet combined models are classy compared to the various time series models in terms of performance basis. Therefore, combining wavelet forecasting models has yielded much better results.

In this research paper, we analyze the flow characteristics of magnetohydrodynamic second grade fluid with heat and mass transfer embedded in porous medium. The modeling of partial differential equations governs the flow have been established with modern approach of Caputo-Fabrizio fractional operator (). The partial differential equations of noninteger order derivatives have been solved by invoking Laplace and Fourier sine transforms. The new analytic solutions for temperature, concentration and velocity are investigated and expressed in terms of simple elementary functions. The corresponding general solutions have been particularized with and without magnetic field and porous medium for the classical Newtonian and second grade fluids as the limiting cases of our general results. The effects of the embedded physical and geometric parameters have been depicted through graphs for velocity, temperature and concentration respectively. The graphical results show several physical discrepancies and analogies on the fluid flow. Finally, our results suggest that increasing the Grashof number, heat transfer due to convection facilitates the flow velocity profile and an opposite trend is observed in thermal Grashof number as well.