Nonlinear Analysis: Modelling and Control
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Existence of a positive solution with concave and convex components for a system of boundary value problems
Full text linkWe prove the existence of at least one positive solution for a system of two nonlinear second-order differential equations with nonlocal boundary conditions. One component of the solution is a concave function, and the other one is a convex function. A recent hybrid Krasnosel’skiĭ–Schauder fixed point theorem is used to prove the existence of a positive solution. To illustrate the applicability of the obtained result, an example is considered
Effect of gravity on the pattern formation in aqueous suspensions of luminous Escherichia coli
Full text linkThis paper presents a nonlinear two-dimensional-in-space mathematical model of self-organization of aqueous bacterial suspensions. The reaction–diffusion–chemotaxis model is coupled with the incompressible Navier–Stokes equations, which are subject to a gravitational force proportional to the relative bacteria density and include a cut-off mechanism. The bacterial pattern formation of luminous Escherichia coli is modelled near the inner lateral surface of a circular microcontainer, as detected by bioluminescence imaging. The simulated plume-like patterns are analysed to determine the values of the dimensionless model parameters, the Schmidt number, Rayleigh number and oxygen cut-off threshold, that closely match the patterns observed experimentally in a luminous E. coli colony. The numerical simulation at the transient conditions was carried out using the finite difference technique
Existence of solution for a fractional differential system on the chemical graph of glycerol
Full text linkIn this paper, we study the chemical graph for an important polyalcoholic compound with the molecular formula C3H8O3 by using 0 or 1 to label the elements of its molecular structure graph and formulating the corresponding fractional boundary value problem on each edge of the graph. Under the sense of Caputo’s fractional derivatives, the existence of solutions of the fractional boundary value problem on the glycerol graph is investigated by introducing some suitable growth conditions and combing with some fixed point theorems. A specific example is given to verify our results
Improved methods for estimation in repeated surveys: Combining time series and calibration
Full text linkThe paper investigates new estimation techniques for repeated surveys, focusing on improving the precision of finite population parameter estimates at the current time t by incorporating auxiliary time series and calibration methods. Repeated surveys generate temporally correlated estimates, which time series models capture effectively. Calibration further enhances estimation by adjusting estimators with auxiliary data, reducing variance, and improving precision. Several new estimators of a time-dependent finite population characteristic (usually the mean, which is used in various statistical analyses) at time t are developed and evaluated under diverse scenarios, considering factors such as the correlation between the errors of the target and auxiliary time series, sampling variance, number of surveys, and model complexity. Numerical results demonstrate that calibrated estimators, particularly those incorporating time series adjustments, achieve superior accuracy in high-correlation settings. Regression-based estimator also shows robust performance across varying conditions, while traditional estimators relying solely on survey data are less precise
On k-fuzzy metric spaces with applications
Full text linkWith application point of view, Gopal et al. [D. Gopal, W. Sintunavarat, A.S. Ranadive, S. Shukla, The investigation of k-fuzzy metric spaces with the first contraction principle in such spaces, Soft Comput., 27:11081–11089, 2023] generalized the conceptions of a fuzzy metric space and introduced the definition of k-fuzzy metric space. Here a fuzzy set defined in k-fuzzy metric space is a membership function FY : X × X × (0, +∞)k -> [0; 1], that is, the fuzzy distance between two points of the set depends on more than one parameter, and then also introduced first contraction principle in this space. In this sequel, we extend the work on k-fuzzy metric spaces by generalizing Banach contraction principle by introducing various type of inequalities. Here we introduce Tirado-type k-fuzzy contraction condition and prove fixed point theorem for Tirado-type contractive mapping. We also discuss the k-fuzzy ψ-contractive mapping, where ψ ∈ Ψ, and Ψ is a class of mappings defined from ψ : [0; 1] -> [0; 1] that has certain properties, and also obtained fixed point for such class of mappings. Later, we define Ćirić-type contraction inequalities to prove fixed point results by restricting ourselves on l-natural property of the fuzzy space to ensure the existence of fixed point. Between all results, a set of supportive examples are also produced to validate the results. In application section, we discuss the solutions of Volterra-type integral equations and second-order nonlinear ordinary differential equation
Dynamic analysis of a fractional-order rumor spreading model with double time delay under higher-order interactions
Full text linkAlthough traditional network-based models also explore higher-order interactions, they are limited in capturing the complex impacts of multibody interactions, making it difficult to characterize the reinforcement effect in rumor propagation. With this in mind, firstly, this study introduces the simplicial complexes, a higher-order mathematical tool, to model rumor propagation. Secondly, the fractional-order derivatives are employed to more accurately capture the memory effect and anomalous diffusion phenomenon in the rumor propagation process under higher-order interactions. Then propagation thresholds and the existence of model solutions are investigated. Moreover, the proposed model exhibits bistability, and the Hopf bifurcation is analysed by choosing time delay as the threshold. Numerical simulations suggest that fractional-order rumor spreading models with higher-order interactions are more consistent with actual data than network-based models and integer-order models
Stability analysis of leptospirosis compartmental model with impact of contaminated environment
Full text linkThe main objective of this article is to analyse the stability properties of a model involving humans, animals and contaminated environment. As a first step, the model is formulated, and its biological well-posedness is proved. Then the basic reproduction number is derived using the next generation matrix (NGM) method. The local and global asymptotic stability of the system at the disease free and endemic equilibrium points are also established. Finally, numerical simulations to illustrate the validity of the theoretical results are performed
Estimations for the convex modular of the aliasing error of nonlinear sampling Kantorovich operators
Full text linkIn this paper, we establish quantitative estimates for the nonlinear sampling Kantorovich operators in the general setting of modular spaces Lρ. To achieve this, we consider a notion of modulus of smoothness based on the convex modular functional ρ, which defines the space. The approach proposed is new in the sense that, in the literature, theorems for the order of approximation in Lρ are mainly qualitative, i.e., are proved considering functions belonging to Lipschitz classes; here the estimates are achieved for every function belonging to the whole Lρ. To show the effectiveness of the achieved results, several particular cases of modular spaces are presented in detail
Computations of local nonsimilar solutions for MHD flow of Reiner–Rivlin fluid
Full text linkHere local nonsimilar solution for hydromagnetic stretched flow of Reiner–Rivlin material is constructed. Heat generation, radiation, and dissipation in thermal expression are studied. Joule heating and chemical reaction of first order are under consideration. Entropy generation is computed. Nonlinear system is derived by adequate transformations. Optimal homotopy analysis technique computes the analysis. Attention is focused to achieve the results of concentration, fluid flow, entropy rate, and temperature. In addition, the skin friction, solutal transport rate and Nusselt number have been explained. Outcomes of magnetic field on velocity and entropy rate are found opposite. Large approximation of fluid parameter improves the fluid flow. Larger estimation of Brinkman number yields same results of entropy generation and temperature. Reduction in concentration is noted through Schmidt number. Higher reaction variable correspond to reduce concentration. Temperature and entropy generation through radiation variable has similar trend. Material variable has similar results for rate of mass transport and coefficient of skin friction. Radiation amplifies the thermal transport rate. Reverse effect for entropy rate and Bejan number is detected for magnetic field
On a sublinear nonlocal fractional problem
Full text linkThis paper deals with existence results of nonnegative solutions for a one-parameter sublinear elliptic boundary-value problem driven by the classical fractional Laplacian operator. The existence of a weak solution for any parameter λ beyond the first resonance has been proved by using a slight variation of the classical Mountain Pass result due to Ambrosetti and Rabinowitz