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ABSTRACT Diving beetles (Coleoptera: Dytiscidae) are general predators that feed primarily on mosquito larvae and can control their populations, but the evidence for such an assumption remains weak. Rhantus elevatus is an important predator of this group distributed in Egypt with both larval and adult stages preying on immature mosquito. For determine predator effectiveness, it is requisite to identify the functional response (a = rate of attack and Th = time of handling) and searching efficacy (at = area of discovery and m = mutual interference) as both correlate with biocontrol efficacy. This study assessed the density‐dependent mortality of Culex pipiens larvae by eliciting functional responses of third‐instar and adult predators at prey density ranging from 100 to 500 larvae per arena. By contrast, a searching efficacy for the same predator stages was examined at densities ranging from one to five predators per 500 prey. Predation rates of third‐instar and adult of R. elevatus were fitted by a model of Type II response with coefficients were: third‐instar (a = 0.208 h−1 and Th = 2413 h) and adult (a = 0.1191 h−1 and Th = 3723 h). The maximum number of mosquitoes which can be devoured by an individual larva and adult of R. elevatus within 24 h was 99.46 and 64.46 prey, respectively. The area of discovery for the larval stage declined more steeply than the adult stage of the predator as their density increased from one to five individuals, indicating more interference estimated for the larval stage. Considering these characteristics, larvae would seem to be the most effective stage against low mosquito populations due to low predation risk compared to that generated at high predator densities in the same arena from intra‐specific interference. Eventually, we suggested a ratio of 1:100 (predator per prey) must be considered in biocontrol plans for mosquitoes. [ABSTRACT FROM AUTHOR]

The primary objective of this study was to explore the behavior of an n-coupled system of generalized Sturm-Liouville (GSL) and Langevin equations under a modified ABC fractional derivative. We aimed to analyze the dynamics of the system and gain insights into how this operator influences the conditions for the existence and uniqueness of solutions. We established the existence and uniqueness of solutions by employing the Banach contraction principle and Leray-Schauder's alternative fixed-point theorem. We also investigated the Hyers-Ulam stability of the system. This analysis allows us to understand the stability properties of the solutions and evaluate their sensitivity to perturbations. Furthermore, we employed Lagrange's interpolation polynomials to produce a numerical scheme for the influenza epidemic model. By combining theoretical analysis, mathematical principles, and numerical simulations, this study contributes to enriching our understanding of the behavior of the system and offers insights into its dynamics and practical applications in epidemiology. [ABSTRACT FROM AUTHOR]

In this paper, we introduce novel extensions of the reversed Minkowski inequality for various functions defined on time scales. Our approach involves the application of Jensen's and Hölder's inequalities on time scales. Our results encompass the continuous inequalities established by Benaissa as special cases when the time scale T corresponds to the real numbers (when T = R). Additionally, we derive distinct inequalities within the realm of time scale calculus, such as cases T = N and qN for q > 1. These findings represent new and significant contributions for the reader. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus by applying the reverse Holder's inequality, integration by parts, and chain rule on time scales nabla calculus. As special cases of our results (when 핋 = ℝ), we get the continuous analouges of inequalities proven by Benaissa and Sarikaya, and when 핋 = ℕ0, the results to the best of the authors' knowledge are essentially new. [ABSTRACT FROM AUTHOR]

This note introduces a new class of preinvexity called (h 1 , h 2) -Godunova-Levin preinvex functions that generalize earlier findings. Based on these notions, we developed Hermite-Hadamard, weighted Fejér, and trapezium type inequalities. Furthermore, we constructed some non-trivial examples in order to verify all the developed results. In addition, we discussed some applications related to the trapezoidal formula, probability density functions, special functions and special means. Lastly, we discussed the importance of order relations and left two open problems for future research. As an additional benefit, we believe that the present work can provide a strong catalyst for enhancing similar existing literature. [ABSTRACT FROM AUTHOR]

In this article, the stochastic Riemann wave equation (SRWE) forced by white noise in the Itô sense is considered. The extended tanh function and mapping methods are applied to obtain new elliptic, rational, hyperbolic, and trigonometric stochastic solutions. Furthermore, we generalize some previous studies. The obtained solutions are important in explaining some exciting physical phenomena, since the SRWE is required for describing wave propagation. We plot numerous 3D and 2D graphical representations to explain how the multiplicative white noise influences the exact solutions of the SRWE. We can infer that the introduction of multiplicative white noise disrupts the symmetry of the solutions and serves to stabilize the solutions of the SRWE. [ABSTRACT FROM AUTHOR]

In this article, we examine the Kraenkel–Manna–Merle system (KMMS) with an M-truncated derivative (MTD). Our goal is to obtain rational, hyperbolic, and trigonometric solutions by using the F -expansion technique with the Riccati equation. To our knowledge, no one has studied the exact solutions to the KMMS in the presence/absence of a damping effect with an M-truncated derivative, using the F -expansion technique. The magnetic field propagation in a zero-conductivity ferromagnet is described by the KMMS; hence, solutions to this equation may provide light on several fascinating scientific phenomena. We use MATLAB to display figures in a variety of 3D and 2D formats to demonstrate the influence of the M-truncated derivative on the exact solutions to the KMMS. [ABSTRACT FROM AUTHOR]