Nonlinear Analysis: Modelling and Control
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Containing an epidemic in the case of running out of treatment: A switched system approach
Full text linkIn this paper, we discuss an epidemic switched system. A susceptible–infected–treated model is considered. The course of an epidemic is profoundly influenced by the allocation of resources. If these resources are limited, then we need to devise an optimal distribution strategy. One significant case to study is when the drug supply is insufficient. We study a control problem that minimizes the total outbreak size of the epidemic and optimizes the rate of vaccination/isolation control by minimizing the suitable functional subject to resource constraints. In the end, simulations are performed for illustrations
A coupled fractional conformable Langevin differential system and inclusion on the circular graph
Full text linkIn this paper, we study a class of coupled fractional conformable Langevin differential system and inclusion on the circular graph. On the one hand, the existence and uniqueness of solutions of this coupled fractional conformable Langevin differential system are studied by fixed point theorems. On the other hand, in the multivalued case, the existence of at least one solution of the fractional conformable Langevin differential inclusion on the circular graph is discussed and the sufficient conditions are established by using Leray–Schauder nonlinear alternative and Covitz–Nadler fixed point theorem
Nontrivial solutions for an asymptotically linear Delta alpha-Laplace equation
No full textIn this paper, we study a class of degenerate unperturbed problems. We first investigate some properties of eigenvalues and eigenfunctions for the strongly degenerate elliptic operator and then obtain two existence theorems of nontrivial solutions when the nonlinearity is a function with an asymptotically condition
Existence of multiple positive solutions for a third-order boundary value problem with nonlocal conditions
Full text linkWe study the existence of multiple positive solutions for a nonlinear third-order differential equation subject to various nonlocal boundary conditions. The boundary conditions that we study contain Stieltjes integral and include the special cases of m-point conditions and integral conditions. The main tool in the proof of our result is Krasnosel’skii’s fixed point theorem. To illustrate the applicability of the obtained results, we consider examples
MHD flow of non-Newtonian ferro nanofluid between two vertical porous walls with Cattaneo–Christov heat flux, entropy generation, and time-dependent pressure gradient
Full text linkThis article studies the magnetohydrodynamic flow of non-Newtonian ferro nanofluid subject to time-dependent pressure gradient between two vertical permeable walls with Cattaneo–Christov heat flux and entropy generation. In this study, blood is considered as non-Newtonian fluid (couple stress fluid). Nanoparticles’ shape factor, Joule heating, viscous dissipation, and radiative heat impacts are examined. This investigation is crucial in nanodrug delivery, pharmaceutical processes, microelectronics, biomedicines, and dynamics of physiological fluids. The flow governing partial differential equations are transformed into the system of ordinary differential equations by deploying the perturbation process and then handled with Runge–Kutta 4th-order procedure aided by the shooting approach. Hamilton–Crosser model is employed to analyze the thermal conductivity of different shapes of nanoparticles. The obtained results reveal that intensifying Eckert number leads to a higher temperature, while the reverse is true for increased thermal relaxation parameter. Heat transfer rate escalates for increasing thermal radiation. Entropy dwindles for intensifying thermal relaxation parameter
An ecoepidemic model with healthy prey herding and infected prey drifting away
Full text linkWe introduce here a predator–prey model where the prey are affected by a disease. The prey are assumed to gather in herds, while the predators are loose and act on an individualistic basis. Therefore their hunting affects mainly the prey individuals occupying the outermost positions in the herd, which is modeled via a square root functional response. The conditions of boundedness and uniform persistence are established. Stability and bifurcation analysis of all feasible equilibrium are carried out. Conditions on the model parameters for the possible existence of limit cycles are derived, global stability analysis is also shown in proper choice of suitable Lyapunov function. Numerical simulation of the various bifurcations validate the theoretical results. It is found that the system ultimate behavior depends mainly on two crucial parameters, the force of infection and predator average handling time. A discussion of the biological significance of the investigation concludes the paper
Cattaneo–Christov heat flux impacts on MHD radiative natural convection of Al2O3-Cu-H2O hybrid nanofluid in wavy porous containers using LTNE
Full text linkThis paper aims to examine impacts of Cattaneo–Christov heat flux on the magnetohydrodynamic convective transport within irregular containers in the presence of the thermal radiation. Both of the magnetic field and flow domain are slant with the inclination angles Ω and γ, respectively. The worked fluid is consisting of water (H2O) and Al2O3-Cu hybrid nanoparticles. The enclosures are filled with a porous medium, and the local thermal nonequilibrium (LTNE) model between the hybrid nanofluids and the porous elements are considered. Influences of various types of the obstacles are examined, namely, horizontal cold elliptic, vertical elliptic and cross section ellipsis. The solution methodology is depending on the finite volume method with nonorthogonal grids. The major outcomes revealed that the location (0.75, 0.5) is better for the rate of the flow and temperature gradients. The higher values of H* causes that the solid phase temperature has a similar behavior of the fluid phase temperature indicating to the thermal equilibrium state. Also, the fluid-phase average Nusselt number is maximizing by increasing Cattaneo–Christov heat flux factor
Stability of port-Hamiltonian systems with mixed time delays subject to input saturation
Full text linkIn this paper, we investigate the stability of port-Hamiltonian systems with mixed time-varying delays as well as input saturation. Three types of time delays, including state delay, input delay, and output delay, are all assumed to be bounded. By introducing the output feedback control law and utilizing serval Lyapunov–Krasovskii functionals, we present three delay-dependent stability criteria in terms of the linear matrix inequality. Meanwhile, we use Wirtinger’s inequality, constraint conditions, and Lyapunov–Krasovskii functionals of triple and quadruple integral form to obtain less conservative results. Some numerical examples demonstrate and support our results
Convergence results based on graph-Reich contraction in fuzzy metric spaces with application
Full text linkThis article introduces a novel class of Reich-type contractions that meet the graph preservation criteria in the context of complete fuzzy metric spaces. The provided contraction condition is satisfied through various forms of contractive mappings via directed graphs in the literature. Our key result is the natural extension of fuzzy metric spaces to fuzzy metrics enriched with a graph, which adds the understanding of fixed points in metric spaces within the realm of graph structure. The findings are further supported by examples and applications
Impact of eye fundus image preprocessing on key objects segmentation for glaucoma identification
Full text linkThe pathological changes in the eye fundus image, especially around Optic Disc (OD) and Optic Cup (OC) may indicate eye diseases such as glaucoma. Therefore, accurate OD and OC segmentation is essential. The variety in images caused by different eye fundus cameras makes the complexity for the existing deep learning (DL) networks in OD and OC segmentation. In most research cases, experiments were conducted on individual data sets only and the results were obtained for that specific data sample. Our future goal is to develop a DL method that segments OD and OC in any kind of eye fundus image but the application of the mixed training data strategy is in the initiation stage and the image preprocessing is not discussed. Therefore, the aim of this paper is to evaluate the mage preprocessing impact on OD and OC segmentation in different eye fundus images aligned by size. We adopted a mixed training data strategy by combining images of DRISHTI-GS, REFUGE, and RIM-ONE datasets, and applied image resizing incorporating various interpolation methods, namely bilinear, nearest neighbor, and bicubic for image resolution alignment. The impact of image preprocessing on OD and OC segmentation was evaluated using three convolutional neural networks Attention U-Net, Residual Attention U-Net (RAUNET), and U-Net++. The experimental results show that the most accurate segmentation is achieved by resizing images to a size of 512 x 512 px and applying bicubic interpolation. The highest Dice of 0.979 for OD and 0.877 for OC are achieved on RISHTI-GS test dataset, 0.973 for OD and 0.874 for OC on the REFUGE test dataset, 0.977 for OD and 0:855 for OC on RIM-ONE test dataset. Anova and Levene’s tests with statistically significant evidence at α = 0.05 show that the chosen size in image resizing has impact on the OD and OC segmentation results, meanwhile, the interpolation method does influent OC segmentation only