In this article, a mathematical model is proposed to define the transmission dynamics of one of the most dangerous plant diseases, citrus canker, by using integer and fractional derivatives. For the fractional-order generalisation, the well-known Caputo fractional derivative is used with the singular-type kernel. The basic features of the proposed integer- and fractional-order models are defined by using well-known mathematical concepts. The proposed model is numerically solved by using the Chebyshev spectral collocation scheme. Some graphical justifications are also given to visualise the disease transmission in the population of citrus plants over time. This research study contains the first non-linear mathematical model of citrus canker transmission, which is the main novelty of this article.

One of the most important disciplines for businesses is production planning. Production planning involves various cost elements such as labor, equipment, raw materials, and inventory while significantly impacting strategic aspects like sales, profit, and market share. Mathematical models used in production planning often address problems of cost minimization or profit maximization. However, besides deterministic-based linear programming applications, it is known that the effect of randomness also plays a significant role in production planning. When parameters are stochastic, meaning random, mathematical models must be capable of generating solutions under the influence of these random parameters. Stochastic modeling developed for problems affected by random parameters can yield the desired results. This study addresses the issue of production planning using stochastic modeling for a company that manufactures industrial-type pipe clamps and has two main product groups. The model that minimizes costs under demand uncertainty uses the Sample Average Approximation (SAA) approach. Initially, a deterministic model was established to obtain the solution when randomness was not included. Subsequently, the stochastic model was solved by creating different scenario sets using SAA, and comparison results were presented.

To develop new conjugate gradient (CG) methods that are both theoretically robust and practically effective for solving unconstrained optimization problems, we propose novel hybrid conjugate gradient algorithms. In these algorithms, the scale parameter β_k is defined as a convex combination of β_k^HZ (from Hager and Zhang’s method) and β_k^BA (from Al-Bayati and Al-Assady’s method). In one hybrid algorithm, the parameter in the convex combination is determined to satisfy the conjugacy condition, independent of the line search. In the other algorithm, the parameter is computed to ensure that the conjugate gradient direction aligns with the Newton direction. Under certain conditions, the proposed methods guarantee a sufficient descent at each iteration and exhibit global convergence properties. Furthermore, numerical results demonstrate that the hybrid computational scheme based on the conjugacy condition is efficient and performs favorably compared to some well-known algorithms.

In this study, the approximated analytical solution for the time-fractional coupled Whitham-Broer-Kaup (WBK) equations describing the propagation of shallow water waves are obtained with the aid of an efficient computational technique called, homotopy analysis Shehu transform methodm(briefly, HASTM). The Caputo operator is utilized to describe fractional-order derivatives. Our proposed approach combines the Shehu transformation with the homotopy analysis method, employing homotopy polynomials to handle nonlinear terms. To validate the correctness of our method, we offer a comparison of obtained and exact solutions with different fractional order values. Given its novelty and straightforward implementation, our method is considered a reliable and efficient analytical technique for solving both linear and non-linear fractional partial differential equations.

Sentiment analysis (SA) plays a critical role in various domains, providing valuable insights into public opinion regarding brands, products, and events. By leveraging this method, companies can enhance customer satisfaction through informed adjustments to their products. This study aims to implement sentiment analysis on user comments from online sales platforms. We propose and evaluate four machine learning (ML) algorithms alongside a deep learning (DL) model. Moreover, our dataset contains noise data that is unsuitable for classification, which negatively impacts performance. To address this issue, feature selection methods are employed to facilitate the algorithms in identifying meaningful patterns more effectively, thereby reducing computational time by focusing on the most contributive features within the dataset. In this context, we apply the binary variant of the Sailfish Optimization Algorithm (SOA), referred to as the Binary Sailfish Optimizer (BSO), as a feature selection technique tailored for our textual dataset, marking its inaugural application in sentiment analysis. To assess the effectiveness of the BSO, we conduct comparative analyses against four other optimization algorithms: Harmony Search (HS), Bat Algorithm (BA), Atom Search Optimization (ASO), and Whale Optimization algorithm (WOA). Our findings indicate that the BSO outperforms the existing algorithms, achieving an F-score of 0.91 while utilizing nearly half of the available features.

In this paper, we investigate a time-dependent conformable Schrödinger equation of order 0 < β ≤ 1, in fractional space domains of space dimension, 0 < D_s ≤ 3. We examine a specific example within the realm of free particle conformable Schrödinger wave mechanics, focusing on both N-Polar and N-Cartesian coordinates systems. We find that the conformable quantities align with the regular counterparts when β = 1.

This paper explores the existence of mild solutions for fuzzy fractional differential equations involving the Hilfer-Katugampola fractional derivative. This derivative generalizes classical fractional derivatives, such as the Riemann-Liouville and Hadamard derivatives, offering a broader framework for fractional calculus. The existence conditions for mild solutions are established using fractional calculus, semigroup theory, and Schauder’s fixed point theorem. An example is provided to demonstrate the theoretical applications of the main results.

The aim of this paper is to establish a robust stability criterion in the Cattaneo-Hristov diffusion equation moving over an interval under the influence of heat sources. The robust stability criterion arises as a generalization of the definition of stability under constant-acting perturbations that is employed in systems of differential equations. The criterion obtained allows to ensure that the solution of the Cattaneo-Hristov diffusion equation and its first partial derivatives with respect to the longitudinal axis and with respect to time can be bounded by a constant whose value is defined a priori. The criterion is illustrated by a numerical example.

This paper investigates the exponential stability of second-order fractional neutral stochastic integral-delay differential equations (FNSIDDEs) with impulses driven by mixed fractional Brownian motions (fBm). Existence and uniqueness conditions ensure that FNSIDDEs are acquired by formulating a Banach fixed point theorem (BFPT). Novel sufficient conditions have to prove p^th moment exponential stability of FNSIDDEs via fBm employing the impulsive-integral inequality. The current study expands and improves on previous findings. Additionally, an example is presented to illustrate the efficiency of the obtained theoretical results.

This paper presents a multi-dimensional vector variational control problem wherein constraints are comprised of first order partial derivatives. As the optimization problems may contain uncertainties driven by measurement and manufacturing errors, erroneous information, irregularities, or perturbations, so the parameter’s randomness is assumed to be in the form of an uncertainty set. Firstly, the sufficient efficiency conditions are demonstrated for the problem under consideration. Then, the Wolfe type and Mond Weir type duals of the primal problem have been formulated. As in multi objective optimization models, attainment of efficient or weak efficient is the primary aim, thus the important robust duality theorems viz. weak, strong and strict converse duality theorems have been established under invexity conditions for Wolfe type dual. An example is also provided to illustrate the weak duality theorem. Thereafter, the duality results for Mond Weir type duals have been obtained under weaker invexity assumptions on involved functionals. This work extends the previously studied results on control problems and hence seeks application in diverse fields.

Due to increasing electricity consumption in Türkiye, energy supply had to increase significantly in the last few decades. As Türkiye has been highly dependent on energy imports, this had an effect on country’s economy. However, especially in the last two decades, Türkiye increased the utilization of renewables. This can significantly improve the energy security and the economy of the country. This paper investigates the development of renewable energy in Türkiye and aims to determine the main drivers behind the significant development recorded in the last decades. In order to do that, past data have been analyzed and a constrained optimization problem has been constructed. This optimization problem aims to minimize the Mean Absolute Error (MAE) between the real and estimated renewable electricity capacity levels in Türkiye. In order to analyze the effect of increasing the number of modeling parameters, this paper considers three cases with different number of modeling parameters. The results in each case reveal the optimum weights and the modeling parameters that should be preferred for modeling the installed renewable energy capacity in Türkiye. The results of the proposed approach, called Mean Absolute Error based OPTimization (MAEOPT), are also compared with that of multiple linear regression (MLR). The obtained MAE values for the best six models reported in this paper (three for MAEOPT and three for MLR) are less than 5%, which indicates an excellent performance. The results also indicate the superiority of MAEOPT over MLR, in terms of MAE and Mean Absolute Percentage Error (MAPE).

The well-known Hermite-Hadamard inequality has attracted the attention of several researchers due to the fact that Hermite-Hadamard inequality has many important applications in mathematics as well as in other areas of science. In this article, the authors present new Hermite-Hadamard inequality of the Mercer type containing Riemann-Liouville k-fractional integrals. For these inequalities, we give integral identity for differentiable functions. With the help of the identity and Hermite-Hadamard-Mercer type inequalities, we derive several results for the inequalities. We establish bounds for the difference of the obtain results by applying Hölder’s inequality and power-mean inequality. We hope that the proposed result will invigorate further interest in this direction.

Metaheuristics have been widely used in recent years for tuning control parameters since they have a simple structure, are easy to apply, and provide efficient solutions. In this study, control of a two-wheeled mobile robot using the inverted pendulum principle is proposed. The performances of nine recent metaheuristics (Political Optimizer, Equilibrium Optimizer, Aquila Optimizer, Flow Directional Algorithm, Cheetah Optimizer, Golden Jackal Optimizer, Artificial Rabbit Optimization, Gazelle Optimizer, and Pelican Optimization) have been investigated for the balancing and speed control of a two-wheeled vehicle. In this context, a framework consisting of two cascaded PI controllers is designed to provide balance and speed control of the two-wheeled vehicle. The performances of the recent metaheuristics are also compared with previously introduced effective metaheuristic algorithms for further evaluation. The parameters of the controllers are tuned by using these metaheuristics. In experimental studies, quantitative and qualitative analyses are performed for evaluation of the metaheuristics. The dynamic system properties, convergence curves, computational times, and statistical results are provided to prove optimal control performances. The results show that 11 out of 14 compared algorithms produce similar optimal results in speed and balance control of the two-wheeled vehicle. The rest of them do not provide satisfactory results for the tuning of optimum control parameters of the two-wheeled vehicle.

This study conducts a comprehensive volatility analysis among firms listed on the BIST100 index using machine learning techniques and panel regression models. Focusing on the period from 2006 to 2023, the study excludes financial firms, resulting in a dataset of 46 companies. The methodology follows a two-step process: First, firms are clustered into low and high-volatility groups using Principal Component Analysis (PCA) and the K-means algorithm; second, panel regression models are applied to determine the financial ratios influencing stock price volatility. The Parkinson Volatility measure is used as the dependent variable, while independent variables include Return on Assets (ROA), Return on Equity (ROE), liquidity ratios, firm beta, and leverage ratios. Results indicate that firm beta has a statistically significant positive impact on volatility across all models, while the current ratio negatively affects volatility in the model 1. These findings provide valuable insights for investors and policymakers regarding risk management in the Turkish stock market. Applying machine learning and advanced econometric techniques adds to the literature on volatility forecasting and financial decision-making.