Groundwater is one of the water resources used to preserve natural water sources for drinking, irrigation, and several other purposes, especially in industrial applications. Human activities related to industry and agriculture result in groundwater contamination. Therefore, investigating water quality is essential for drinking and irrigation purposes. In this work, the water quality index (WQI) was used to identify the suitability of water for drinking and irrigation. However, generating an accurate WQI requires much time, as errors may be made during the sub-index calculations. Hence, an artificial intelligence (AI) prediction model was built to reduce both time and errors. Eighty data samples were collected from Sakrand, a city in the province of Sindh, to investigate the area’s WQI. The classification learners were used with raw data samples and the normalized data to select the best classifier among the following decision trees: support vector machine (SVM), k-nearest neighbors (K-NN), ensemble tree (ET), and discrimination analysis (DA). These were included in the classification learner tool in MATLAB. The results revealed that SVM was the best raw and normalized data classifier. The prediction accuracy levels for the training data were 90.8% and 89.2% for the raw and normalized data, respectively. Meanwhile, the prediction accuracy levels for the testing data were 86.67 and 93.33% for the raw and normalized data, respectively.

The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other fields of mathematical physics and engineering. This study has two main objectives. First, the main objective of this investigation is to solve the fractional-order nonlinear Gardner and Cahn–Hilliard equations by using the modified auxiliary equation method, which is not found in the literature. Second, the exact and approximate solutions of these equations are obtained by utilizing the fractional conformable residual power series algorithm and the modified auxiliary equation method. For the analytical and numerical solutions to two equations, we employ two separate techniques and establish consistency between the precise answers that are derived and the compatible numerical solution. To the best of our knowledge, this method of solving equations has never been investigated in this manner. The 2D and 3D contours have been defined using appropriate parametric values to support the physical compatibility of the results. The assessed findings suggested that the approach used in this study to recover inclusive and standard solutions is approachable, efficient, and faster in computing and can be considered a useful tool in resolving more complex phenomena that arise in the field of engineering, mathematical physics, and optical fiber.