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In this paper, with the use of newly defined class up and down log–convex fuzzy-number valued mappings, we offer a few new and original mappings defined by applying some mild restrictions over the definition of up and down log–convex fuzzy-number valued mapping. With the use of these mappings, we are able to develop partners of Fejér-type inequalities for up and down log–convexity, which improve upon certain previously established findings. The discussion also includes these mappings’ characteristics. Moreover, some nontrivial examples are also provided to prove the validation of our main results.

In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We studied the stability of the fixed points in the discrete cancer system using the new version of Marotto’s theorem at a fixed point; we prove that the discrete cancer system is chaotic. Finally, we present numerical simulations, e.g., Lyapunov exponents and bifurcations diagrams.

The current study focuses on the natural-convection flow of nanofluids with boundary layer over a circular cylinder of uniform thermal wall with varying magnetic force from 0 to 1.5, radiative effects from 0 to 1, heat generation effects from 0 to 1, and Joule heating effects from 0 to 1. The problem is represented in the form of partial differential equations. The dimensional form of the equations is converted into a dimensionless form with the help of suitable stream functions. Then, the resultant equations are further reduced into the system of first-ordered differential equations, and the Keller box scheme is applied to obtain a solution numerically with the help of MATLAB code. The numerical solutions for Nusselt number, skin friction coefficient, Sherwood number, velocity profile, temperature profile, and concentration profile are represented with the help of graphs. The most interesting fact of the analysis is the flow of the fluid; the heat-mass and energy transfer rates could be managed in a controlled way through slight variations in the Brownian motion parameter from 0.1 to 0.7, in the Lewis number from 1 to 40, in the Eckert number from 0.1 to 0.4, in the thermophoresis parameter from 0.1 to 0.7, in the Prandtl number from 0.1 to 0.7, and in the buoyancy ratio from 0.1 to 0.7, as it is here analyzed and discussed.

Alzheimer’s disease (AD) is a growing public health crisis, a very global health concern, and an irreversible progressive neurodegenerative disorder of the brain for which there is still no cure. Globally, it accounts for 60–80% of dementia cases, thereby raising the need for an accurate and effective early classification. The proposed work used a healthy aging dataset from the USA and focused on three transfer learning approaches: VGG16, VGG19, and Alex Net. This work leveraged how the convolutional model and pooling layers work to improve and reduce overfitting, despite challenges in training the numerical dataset. VGG was preferably chosen as a hidden layer as it has a more diverse, deeper, and simpler architecture with better performance when dealing with larger datasets. It consumes less memory and training time. A comparative analysis was performed using machine learning and neural network algorithm techniques. Performance metrics such as accuracy, error rate, precision, recall, F1 score, sensitivity, specificity, kappa statistics, ROC, and RMSE were experimented with and compared. The accuracy was 100% for VGG16 and VGG19 and 98.20% for Alex Net. The precision was 99.9% for VGG16, 96.6% for VGG19, and 100% for Alex Net; the recall values were 99.9% for all three cases of VGG16, VGG19, and Alex Net; and the sensitivity metric was 96.8% for VGG16, 97.9% for VGG19, and 98.7% for Alex Net, which has outperformed when compared with the existing approaches for the classification of Alzheimer’s disease. This research contributes to the advancement of predictive knowledge, leading to future empirical evaluation, experimentation, and testing in the biomedical field.

The term hotspot refers to a location or an area where the occurrence of a particular phenomenon, event, or activity is significantly higher than in the surrounding areas. The existing statistical methods need help working well on discrete data. Also, it can identify a false hotspot. This paper proposes a novel graph-based hotspot detection using a rough set (GBHSDRS) for detecting the hotspots. This algorithm works well with discrete spatial vector data. Furthermore, it removes the false hotspot by finding the statistical significance of the identified hotspots. A rough set theory is applied to the graph of the spatial polygon data, and the nodes are divided into lower, boundary, and negative regions. Therefore, the candidate hotspot belongs to the lower region of the set, and the boundary value analysis will ensure the identification of the hotspots if the hotspot is present in the dataset. The p-value is used to find the statistical significance of the hotspots. The algorithm is tested on the socioeconomic data of Uttar Pradesh (UP) from 1991 on medical facilities. The average gain in density and Hotspot Prediction Accuracy Index (HAPI) of the detected hotspots is 26.54% and 23.41%, respectively. An average reduction in runtime is 27.73%, acquired compared to all other methods on the socioeconomic data.

The aim of this paper is to introduce new forms of quasi-contractions in metric-like spaces and initiate more general conditions for the existence of invariant points for such operators. The proposed notions are then applied to study novel existence criteria for the existence of solutions to two-point boundary value problems in the domains of integer and fractional orders. To attract further research in this direction, important consequences are deduced and discussed to indicate the novelty and generality of our proposed concepts.

A lot of work has been completed in efforts to extend the notions of soft set and fuzzy soft set and their applications to other domains. However, neither of the two concepts has been examined in the study of functional equations in b-metric spaces. Given this background information, this paper proposes the idea of b-hybrid fuzzy soft contraction in b-metric space and investigates new criteria for the existence of fixed points for such mappings. The significance of the obtained principal result lies in the fact that the contractive inequalities can be specialized in various ways, depending on the choice of the parameters, thereby making it possible to unify, deduce, and refine several corresponding results. To motivate further studies in the directions studied herein, two applications regarding decision-making problems and an existence theorem of integral inclusion are considered, using fuzzy soft set-valued maps.

In this work, the class of nonlinear complex fractional Kundu-Eckhaus equation is presented with a novel truncated M-fractional derivative. This model is significant and notable in quantum mechanics with good-natured physical characteristics. The motivation for this paper is to construct new solitary and kink wave solutions for the governing equation using the ansatz method. A complex-fractional transformation is applied to convert the fractional Kundu-Eckhaus equation into an ordinary differential equations system. The equilibria of the corresponding dynamical system will be presented to show the existence of traveling wave solutions for the governing model. A novel kink and solitary wave solutions of the governing model are realized by means of the proposed method. In order to gain insight into the underlying dynamics of the obtained solutions, some graphical representations are drawn. For more illustration, several numerical applications are given and analyzed graphically to demonstrate the ability and reliability of the method in dealing with various fractional engineering and physical problems.

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In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons is specifically analyzed through numerical calculation at certain boundary conditions. This study revels sufficient analytical description for radial flux distribution of multi-energy groups of neutron diffusion theory as well as determination of each nuclear reactor dimension in criticality case. The generated results are compatible with other different methods data. The generated results are practically efficient for neutron reactors dimension.