Artificial intelligence applications based on soft computing and machine learning algorithms have recently become the focus of researchers’ attention due to their robustness, precise modeling, simulation, and efficient assessment. The presented work aims to provide an innovative application of Levenberg Marquardt Technique with Artificial Back Propagated Neural Networks (LMT-ABPNN) to examine the entropy generation in Marangoni convection Magnetohydrodynamic Second Grade Fluidic flow model (MHD-SGFM) with Joule heating and dissipation impact. The PDEs describing MHD-SGFM are reduced into ODEs by appropriate transformation. The dataset is determined through Homotopy Analysis Method by the variation of physical parameters for all scenarios of proposed LMT-ABPNN. The reference data samples for training/validation/testing processes are utilized as targets to determine the approximated solution of proposed LMT-ABPNN. The performance of LMT-ABPNN is validated by MSE based fitness, error histogram scrutiny, and regression analysis. Furthermore, the influence of pertinent parameters on temperature, concentration, velocity, entropy generation, and Bejan number is also deliberated. The study reveals that the larger $\beta$ and $Ma$, the higher $f^{\prime }\left(\eta \right)$ while $M$ has the reverse influence on $f^{\prime }\left(\eta \right).$ For higher values of $\beta , M, Ma,$ and $Ec$, $\theta \left(\eta \right)$ boosts. The concentration $\varphi \left(\eta \right)$ drops as Ma and Sc grow. An augmentation is noticed for $N_{G }$for higher estimations of $\beta ,M,$ and $Br$. Larger $\beta ,M$ and $Br$ decays the Bejan number.

In the present paper, we aimed to discuss certain coefficient-related problems for the inverse functions associated with a bounded turning functions class subordinated with the exponential function. We calculated the bounds of some initial coefficients, the Fekete–Szegö-type inequality, and the estimation of Hankel determinants of second and third order. All of these bounds were proven to be sharp.

The purpose of this article is to obtain the sharp estimates of the first four initial logarithmic coefficients for the class ${\mathcal{BT}}_s$ of bounded turning functions associated with a petal-shaped domain. Further, we investigate the sharp estimate of Fekete-Szegö inequality, Zalcman inequality on the logarithmic coefficients and the Hankel determinant $H_{2,1}\left(F_f/2\right)$ and $H_{2,2}\left(F_f/2\right)$ for the class ${\mathcal{BT}}_s$ with the determinant entry of logarithmic coefficients.