This research introduces a model of a delayed reaction–diffusion fractional neural network with time-varying delays. The Mittag–Leffler-type stability of the solutions is investigated, and new sufficient conditions are established by the use of the fractional Lyapunov method. Mittag–Leffler-type synchronization criteria are also derived. Three illustrative examples are established to exhibit the proposed sufficient conditions.

In the paper, a class of impulsive Caputo fractional-order bi-directional associative memory neural networks with time-varying delays is considered. Applying the fractional Lyapunov method, a sufficient condition for Mittag-Leffler stability of the equilibrium point of the system under consideration is derived. Some earlier results are extended and improved. Our results provide an impulsive control law which stabilizes the impulse-free fractional-order neural network time-delay model. An example is provided to demonstrate the effectiveness of the proposed results.

The exactitude of petroleum fluid molecular weight correlations affects significantly the precision of petroleum engineering calculations and can make process design and trouble-shooting inaccurate. Some of the methods in the literature to predict petroleum fluid molecular weight are used in commercial software process simulators. According to statements made in the literature, the correlations of Lee–Kesler and Twu are the most used in petroleum engineering, and the other methods do not exhibit any significant advantages over the Lee–Kesler and Twu correlations. In order to verify which of the proposed in the literature correlations are the most appropriate for petroleum fluids with molecular weight variation between 70 and 1685 g/mol, 430 data points for boiling point, specific gravity, and molecular weight of petroleum fluids and individual hydrocarbons were extracted from 17 literature sources. Besides the existing correlations in the literature, two different techniques, nonlinear regression and artificial neural network (ANN), were employed to model the molecular weight of the 430 petroleum fluid samples. It was found that the ANN model demonstrated the best accuracy of prediction with a relative standard error (RSE) of 7.2%, followed by the newly developed nonlinear regression correlation with an RSE of 10.9%. The best available molecular weight correlations in the literature were those of API (RSE = 12.4%), Goosens (RSE = 13.9%); and Riazi and Daubert (RSE = 15.2%). The well known molecular weight correlations of Lee–Kesler, and Twu, for the data set of 430 data points, exhibited RSEs of 26.5, and 30.3% respectively.

Forty-eight crude oils with variations in specific gravity (0.782 ≤ SG ≤ 1.002), sulphur content (0.03 ≤ S ≤ 5.6 wt.%), saturate content (23.5 ≤ Sat. ≤ 92.9 wt.%), asphaltene content (0.1 ≤ As ≤ 22.2 wt.%), and vacuum residue content (1.4 ≤ VR ≤ 60.7 wt.%) were characterized with HTSD, TBP, and SARA analyses. A modified SARA analysis of petroleum that allows for the attainment of a mass balance ≥97 wt.% for light crude oils was proposed, a procedure for the simulation of petroleum TBP curves from HTSD data using nonlinear regression and Riazi’s distribution model was developed, and a new correlation to predict petroleum saturate content from specific gravity and pour point with an average absolute deviation of 2.5 wt.%, maximum absolute deviation of 6.6 wt.%, and bias of 0.01 wt.% was developed. Intercriteria analysis was employed to evaluate the presence of statistically meaningful relations between the different petroleum properties and to evaluate the extent of similarity between the studied petroleum crudes. It was found that the extent of similarity between the crude oils based on HTSD analysis data could be discerned from data on the Kw characterization factor of narrow crude oil fractions. The results from this study showed that contrary to the generally accepted concept of the constant Kw characterization factor, the Kw factors of narrow fractions differ from that of crude oil. Moreover, the distributions of Kw factors of the different crudes were different.