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This paper presents a new SIRS model for recurrent childhood diseases under the Caputo fractional difference operator. The existence theory is established using Brouwer's fixed-point theorem and the Banach contraction principle, providing a comprehensive mathematical foundation for the model. Ulam stability is demonstrated using nonlinear functional analysis. Sensitivity analysis is conducted based on the variation of each parameter, and the basic reproduction number (R 0) is introduced to assess local stability at two equilibrium points. The stability analysis indicates that the disease-free equilibrium point is stable when R 0 < 1 , while the endemic equilibrium point is stable when R 0 > 1 and otherwise unstable. Numerical simulations demonstrate the model's effectiveness in capturing realistic scenarios, particularly the recurrent patterns observed in some childhood diseases. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model to lower the probability of breast cancer risk of the Breast Imaging Reporting and Data Systems (BI-RADS) 4 subcategories with the fractal fractional operator. This method improves evaluation quality, creates straightforward concepts for the early detection of breast cancer, and outcomes can be tracked easily by using BI-RADS-4 subcategories data at the Near East University Hospital. It uses the Banach fixed point theorem for nonlinear functional analysis and confirms the boundedness and uniqueness of solutions. Sensitivity analysis was performed on model parameters, and advanced numerical techniques were used to develop solutions. Also, this reveals disease-free and endemic equilibrium points, indicating local and global asymptotic stability. Chaos control was used in the regulated for linear responses approach to bring the system to stabilize according to its points of equilibrium. The growing procedure yields more effective and similar outcomes than the rotting technique, which happens quickly in the lowest fractional orders. Using Lagrange polynomial insight into the fractal-fractional operator, we conducted simulations and presented a comparative analysis in graphical form with classical and non-integer derivatives. The comparison of integer and non-integer results highlighted the importance of accurate fractional parameters in simulation. Moreover, it suggests that fractional operator-included mathematical models can help reveal more significant decisions on managing such real-life problems. Numerical simulations reveal absorption features for the fractal-fractional derivative with a generalized Mittag-Leffler kernel. The approximation solution approach allows for different order and dimension between 0 and 1, with outcomes changing for different fractional and fractal orders. It was determined that early diagnosis, quitting smoking, higher lactation rates, and ongoing care can reduce cancer risk. Our findings are critical for researchers, policymakers, and health care practitioners in combating and preventing breast cancer, contributing to worldwide public health initiatives. • The (BI-RADS) is intended to standardize reporting on breast imaging. • Model was tested on 42 BI-RADS 4 patients at NEU Hospital, demonstrating converging characteristics. • It uses the Banach fixed point theorem for nonlinear functional analysis. • Disease-free and endemic equilibrium points, indicating local and global asymptotic stability. • Sensitivity analysis is performed, and advanced numerical techniques are used to develop solutions. [ABSTRACT FROM AUTHOR]

The family F (U) of all fuzzy sets in a normed space cannot be a vector space. This deficiency affects its application to practical problems. The topics of functional analysis and nonlinear analysis in mathematics are based on vector spaces. Since these two topics have been well developed such that their tools can be used to solve practical economics and engineering problems, lacking a vector structure for the family F (U) diminishes its applications to these kinds of practical problems when fuzzy uncertainty has been detected in a real environment. Embedding the whole family F (U) into a Banach space is still not possible. However, it is possible to embed some interesting and important subfamilies of F (U) into some suitable Banach spaces. This paper presents the concrete and detailed structures of these kinds of Banach spaces such that their mathematical structures can penetrate the core of practical economics and engineering problems in fuzzy environments. The important issue of uniqueness for these Banach spaces is also addressed via the concept of isometry. [ABSTRACT FROM AUTHOR]

This article is dedicated to presenting and discussing various results, including several new findings, directly or indirectly related to Bolzano's theorem, famously known as the intermediate value theorem, and its multi- or infinite-dimensional versions. We aim to provide a unified approach to these issues, consistently relying on the concept of tangency. The paper seeks to justify that tangency, a geometric property, firmly supported by appropriate topological arguments, constitutes one of the central tools in nonlinear functional analysis. Our objective is to demonstrate that the legacy of Bolzano and his followers remains significant and vibrant, constituting one of the cornerstones of contemporary mathematics. [ABSTRACT FROM AUTHOR]

In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional order derivatives. A complementary method involves analyzing the system of fractal fractional order equations by considering the set of symmetries of its solutions. By characterizing structures that relate to the fundamental dynamics of biological systems, symmetries offer a potent notion for the creation of mechanistic models. This study investigates a novel mathematical model for conjunctivitis adenovirus disease. Conjunctivitis is an infection in the eye that is caused by adenovirus, also known as pink eye disease. Adenovirus is a common virus that affects the eye's mucosa. Infectious conjunctivitis is most common eye disease on the planet, impacting individuals across all age groups and demographics. We have formulated a model to investigate the transmission of the aforesaid disease and the impact of vaccination on its dynamics. Also, using mathematical analysis, the percentage of a population which needs vaccination to prevent the spreading of the mentioned disease can be investigated. Fractal fractional derivatives have been widely used in the last few years to study different infectious disease models. Hence, being inspired by the importance of fractal fractional theory to investigate the mentioned human eye-related disease, we derived some adequate results for the above model, including equilibrium points, reproductive number, and sensitivity analysis. Furthermore, by utilizing fixed point theory and numerical techniques, adequate requirements were established for the existence theory, Ulam–Hyers stability, and approximate solutions. We used nonlinear functional analysis and fixed point theory for the qualitative theory. We have graphically simulated the outcomes for several fractal fractional order levels using the numerical method. [ABSTRACT FROM AUTHOR]

Recently, the area devoted to fractional calculus has given much attention by researchers. The reason behind such huge attention is the significant applications of the mentioned area in various disciplines. Different problems of real world processes have been investigated by using the concepts of fractional calculus and important and applicable outcomes were obtained. Because, there has been a lot of interest in fractional differential equations. It is brought on by both the extensive development of fractional calculus theory and its applications. The use of linear and quadratic perturbations of nonlinear differential equations in mathematical models of a variety of real-world problems has received a lot of interest. Therefore, motivated by the mentioned importance, this research work is devoted to analyze in detailed, a class of fractal hybrid fractional differential equation under Atangana- Baleanu- Caputo ABC derivative. The qualitative theory of the problem is examined by using tools of non-linear functional analysis. The Ulam-Hyer's (U-H) type stability criteria is also applied to the consider problem. Further, the numerical solution of the model is developed by using powerful numerical technique. Lastly, the Wazewska-Czyzewska and Lasota Model, a well-known biological model, verifies the results. Several graphical representations by using different fractals fractional orders values are presented. The detailed discussion and explanations are given at the end. [ABSTRACT FROM AUTHOR]

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie "non-computational" proofs from the mainstream literature. To this end, we establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches. [ABSTRACT FROM AUTHOR]

Objective: In the past, the localization of seizure onset zone (SOZ) primarily relied on traditional EEG signal analysis methods. However, due to their limited spatial and temporal resolution, accurately pinpointing neural activity was challenging, thereby restricting their clinical applicability. Compared with traditional EEG signals, SEEG signals have superior spatial and temporal resolution, and can more accurately record neural activity near epileptic foci, making them better suited for studying SOZ. In addition, the traditional EEG signal analysis methods still have limitations, mainly focusing on the analysis of local signal features, while ignoring the complexity and interconnection of the overall brain network. How to more accurately locate SOZ is still not well resolved. The purpose of this study is to develop an effective positioning method for more accurate positioning. Method: To overcome these limitations, this study proposed a model integrating brain functional network analysis with nonlinear dynamics. We utilized weighted phase lag index (WPLI) to construct brain functional network, epilepic network connectivity strength (ENCS) as the feature, and introduced persistence entropy (PE) for feature fusion, subsequently employing support vector machine (SVM) classification. Results: The proposed method was verified on the HUP-iEEG dataset, our solution identified the SOZ with 0.9440 accuracy, 0.9848 precision, 0.8974 recall rate, 0.9340 F1 score and 0.9697 area under the ROC curve across patients, which outperforms the existing approaches. It exhibits a 2.30 percentage point enhancement in localisation accuracy along with a 2.97 percentage points in AUC compared to others. Conclusion: Our method consider the interactions between nodes in brain network connections, as well as the inherent nonlinear and non-stationary properties of neural signals, to be more robust. [ABSTRACT FROM AUTHOR]

This manuscript investigates the existence, uniqueness, and different forms of Ulam stability for a system of three coupled differential equations involving the Riemann–Liouville (RL) fractional operator. The Leray–Schauder alternative is employed to confirm the existence of solutions, while the Banach contraction principle is used to establish their uniqueness. Stability conditions are derived utilizing classical nonlinear functional analysis techniques. Theoretical findings are illustrated with an example. The proposed system generalizes third-order ordinary differential equations (ODEs) with different boundary conditions (BCs). [ABSTRACT FROM AUTHOR]

In this dissertation, we study the coupled system of q$$ q $$‐fractional Langevin differential equations involving q$$ q $$‐Caputo derivative having q$$ q $$‐fractional integral conditions. With the help of some adequate conditions, we investigate the uniqueness and existence of mild solution of the aforementioned system. We also analyze various kinds of Ulam's stability. Banach fixed point theorem and Leray–Schauder of cone type are used to illustrate the existence and uniqueness results. We also used non‐linear functional analysis methods to explore variety of stability types. An example is provided to clearly demonstrate our theoretical outcomes. [ABSTRACT FROM AUTHOR]

In order to develop the basic theory of resonance boundary value problems for nonlinear quantum difference equations, a class of nonlinear quantum difference equation boundary value problems at resonance on infinite intervals was studied. Firstly, by constructing a suitable Banach space, the Fredholm operator was defined, and its kernel and value domains were obtained. Secondly, by defining other appropriate operators, and using Mawhin′s coincidence degree theory, the existence theorem of solutions to this problem was established. Thirdly, the uniqueness of the solution was obtained by means of proof by contradiction. Finally, an example was given to illustrate the validity of the main results. The results show that under certain growth conditions of nonlinear terms, the boundary value problems for nonlinear quantum difference equation at resonance has at least one solution. The research results enrich the solvability theory of quantum difference equations, and provide important theoretical basis for the application of quantum difference equations in mathematics, physics and other fields.

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model's intricate dynamics. [ABSTRACT FROM AUTHOR]

The excessive use of drugs has become a growing concern in the current century, with the global toll of drug-related deaths and disabilities posing a significant public health challenge in both developed and developing countries. In pursuit of continuous improvement in existing strategies, this article presented a nonlinear deterministic mathematical model that encapsulates the dynamics of drug addiction transmission while considering the legal implications imposed by criminal law within a population. The proposed model incorporated the fractal-fractional order derivative using the Atangana-Baleanu-Caputo (ABC) operator. The objectives of this research were achieved by examining the dynamics of the drug transmission model, which stratifies the population into six compartments: The susceptible class to drug addicts, the number of individuals receiving drug misuse education, the count of mild drug addicts, the population of heavy-level drug addicts, individuals subjected to criminal law, and those who have ceased drug use. The qualitative analysis of the devised model established the existence and uniqueness of solutions within the framework of fixed-point theory. Furthermore, Ulam-Hyer's stability was established through nonlinear functional analysis. To obtain numerical solutions, the fractional Adam-Bashforth iterative scheme was employed, and the results were validated through simulations conducted using MATLAB. Additionally, numerical results were plotted for various fractional orders and fractal dimensions, with comparisons made against integer orders. The findings underscored the necessity of controlling the effective transmission rate to halt drug transmission effectively. The newly proposed strategy demonstrated a competitive advantage, providing a more nuanced understanding of the complex dynamics outlined in the model. [ABSTRACT FROM AUTHOR]

A mathematical model of progressive disease of the nervous system also called multiple sclerosis (MS) is studied in this paper. The proposed model is investigated under the concept of the fractal-fractional order derivative (FFOD) in the Caputo sense. In addition, the tools of nonlinear functional analysis are applied to prove some qualitative results including the existence theory, stability, and numerical analysis. For the recommended results of the existence theory, Banach and Krassnoselski's fixed point theorems are used. Additionally, Hyers–Ulam (HU) concept is used to derive some results for stability analysis. Additionally, for numerical illustration of approximate solutions of various compartments of the considered model, the modified Euler method is utilized. The aforementioned results are displayed graphically for various values of fractal-fractional orders. [ABSTRACT FROM AUTHOR]

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The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mappings in Hausdorff p-vector spaces, and a fixed point theorem for upper semicontinuous set-valued mappings in locally p-convex spaces for p 2 (0; 1]. These results not only provide a solution to Schauder conjecture in the affirmative under the setting of p-vector spaces for compact single-valued continuous mappings, but also show the existence of fixed points for upper semicontinuous set-valued mappings defined on s-convex subsets in Hausdorff locally p-convex spaces, which would be fundamental for nonlinear functional analysis, where s; p 2 (0; 1]. [ABSTRACT FROM AUTHOR]

In this work, a system of nonlinear, switched, coupled, implicit, impulsive Langevin equations with two Hilfer fractional derivatives is introduced. The suitable conditions and results are established to discuss existence, uniqueness, and Ulam-type stability results of the mentioned model, with the help of nonlinear functional analysis techniques and Banach's fixed-point theorem. Furthermore, we examine our results with the help of example. [ABSTRACT FROM AUTHOR]

Conditions for the existence of a symmetric solution of nonlinear functional differential equations with symmetries are established. [ABSTRACT FROM AUTHOR]

This research paper focuses on investigating the solvability of a constrained problem involving a nonlinear delay functional equation subject to a quadratic functional integral constraint, in two significant cases: firstly, the existence of nondecreasing solutions in a bounded interval L 1 [ 0 , T ] and, secondly, the existence of nonincreasing solutions in unbounded interval L 1 (R +) . Moreover, the paper explores various qualitative properties associated with these solutions for the given problem. To establish the validity of our claims, we employ the De Blasi measure of noncompactness (MNC) technique as a basic tool for our proofs. In the first case, we provide sufficient conditions for the uniqueness of the solution ψ ∈ L 1 [ 0 , T ] and rigorously demonstrate its continuous dependence on some parameters. Additionally, we establish the equivalence between the constrained problem and an implicit hybrid functional integral equation (IHFIE). Furthermore, we delve into the study of Hyers–Ulam stability. In the second case, we examine both the asymptotic stability and continuous dependence of the solution ψ ∈ L 1 (R +) on some parameters. Finally, some examples are provided to verify our investigation. [ABSTRACT FROM AUTHOR]

In this work, we study a dynamic model of social media addiction. Addiction to social media is a behavioral addiction that is very complex in nature. To study such kinds of complex behavior, the fractional-order operators are very useful due to their memory nature. Considering all these facts, we consider the fractional and fractal-fractional operators with a singular kernel to investigate the social media addiction model. This paper's main aim is to demonstrate the importance of non-classical-order derivatives in the investigation of the social media addiction model. First, we propose the model using Caputo fractional derivative and present some basic mathematical computations. The existence condition for a solution of the model system is presented via fixed-point theory. Furthermore, the behavior of the social media addiction model is examined using the fractal-fractional concept with the Caputo operator, which, due to its memory effect, is very effective in modeling. The existence and uniqueness of the solution are investigated using fixed point theory. Ulam–Hyers stability is demonstrated using nonlinear functional analysis. We demonstrate the simulated numerical results graphically for the proposed models via numerical methods based on Lagrange polynomial interpolation. The results are plotted for choices of arbitrary-order parameter values. Based on our findings, we can say the fractal-fractional operators provide more realistic information about the complexity of the dynamics of the social media addiction model. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate Korteweg–De Vries equations (KDVEs) with third order under fractional Atangana–Baleanu–Caputo (ABC) derivative. We use an analytical method due to the Laplace transform and the Adomian decomposition technique. We establish the convergence analysis results for the considered problem by using nonlinear functional analysis. First of all, a general algorithm is developed for the computation of the required analytical approximate solution by using the mentioned method. By applying the developed algorithm, we then investigate the approximate solutions for some examples. The computed solution has also been presented graphically using Matlab. Laplace Adomian decomposition method (LADM) is a powerful full technique that is easy to implement. In addition, the said method has also a fast convergent quality. [ABSTRACT FROM AUTHOR]

In this manuscript, switched coupled system of nonlinear impulsive Langevin equations involving four Hilfer fractional-order derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss the existence, uniqueness, and Ulam's type stability results of our proposed model, with the help of Schaefer's fixed point theorem. An example is provided at the end to illustrate our results. [ABSTRACT FROM AUTHOR]

The paper provides an overarching framework for the study of some of the intrinsic geometries that a topological group may carry. An initial analysis is based on geometric nonlinear functional analysis, that is, the study of Banach spaces as metric spaces up to various notions of isomorphism, such as bi-Lipschitz equivalence, uniform homeomorphism, and coarse equivalence. This motivates the introduction of the various geometric categories applicable to all topological groups, namely, their uniform and coarse structure, along with those applicable to a more select class, that is, (local) Lipschitz and quasimetric structure. Our study touches on Lie theory, geometric group theory, and geometric nonlinear functional analysis and makes evident that these can all be seen as instances of a single coherent theory. [ABSTRACT FROM AUTHOR]

The given text is a research article that investigates the regularity of weak solutions to the compressible Navier-Stokes-Poisson equations. The authors develop estimates for the velocity using the Moser iteration method and Gronwall inequality. The article provides preliminary results and presents a prior L1 estimate of the velocity. The authors aim to contribute to the understanding of the regularity of weak solutions to these equations. The text is aimed at researchers or mathematicians studying this specific problem or topic. [Extracted from the article]

This paper deals with the existence, uniqueness and Ulam-stability outcomes for (...)-Hilfer fractional fuzzy differential equations with impulse. Further, by using the techniques of nonlinear functional analysis, we study the Ulam-Hyers-Rassias stability. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the Dirichlet problem for semi-linear Stokes equations. The approach of this study is based on the operator method, using abstract results of nonlinear functional analysis. We first study the problem using Schauder's fixed point theorem and we prove the existence of a solution in case that the nonlinear term has a linear growth. Next we establish whether the existence of solutions can still be obtained without this linear growth restriction. Such a result is obtained by applying the Leray-Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

This paper investigates a class of nonlinear impulsive fractional integro-differential equations with mixed nonlocal boundary conditions (multi-point and multi-term) that involves (k, k)- Hilfer fractional derivative. The main objective is to prove the existence and uniqueness of the solution for the considered problem by means of fixed point theory of Banach's and O'Regan's types, respectively. In this contribution, the transformation of the considered problem into an equivalent integral equation is necessary for our main results. Furthermore, the nonlinear functional analysis technique is used to investigate various types of Ulam's stability results. The applications of main results are guaranteed with three numerical examples. [ABSTRACT FROM AUTHOR]

This article considers the existence and the uniqueness of monotonic solutions of a delay functional integral equation of fractional order in the weighted Lebesgue space LN 1 (R+). Our analysis uses a suitable measure of noncompactness, a modified version of Darbo's fixed point theorem, and fractional calculus in the mentioned space. An illustrated example to show the applicability and significance of our outcomes is included. [ABSTRACT FROM AUTHOR]

The solutions to fractional differential equations are a developing area of current research, given that these equations arise in various domains. In this article, we provide some necessary criteria for the existence, uniqueness, and different types of Ulam stability for a coupled implicit system requiring the conditions for nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions. The uniqueness and existence results for the suggested coupled system are demonstrated using Banach fixed point theorem and Leray–Schauder of cone type. We also explore the various types of stability using classical methods of nonlinear functional analysis. To verify the effectiveness of our theoretical outcomes, we study an interesting example. [ABSTRACT FROM AUTHOR]

A mathematical epidemiological model for the transmission of Hepatitis B virus in the frame of fractional derivative with harmonic mean type incidence rate is proposed in this article. The proposed mathematical model is then fictionalized by utilizing the Atangana–Baleanu–Capotu ( A B C ) operator with vaccination effects. The threshold number R0 is calculated by utilizing the next-generation matrix approach. The existence and uniqueness of solution of the proposed model are proved by utilizing the well-known fixed point theory. For the numerical solution of the proposed model with A B C derivative the well-known Adams–Bashforth–Molton (ABM) method is utilized. Likewise, stability is required in regard of the numerical arrangement. In this manner, Ulam–Hyers stability utilizing nonlinear functional analysis is utilized for the proposed model. [ABSTRACT FROM AUTHOR]

Data from measurements over time can be analyzed in different ways. In this article, we compare functional data analysis and nonlinear regression models using, among others, eight information quality dimensions. We present two case studies. The first case study introduces functional data analysis and nonlinear regression models in analyzing dissolution profiles of drug tablets where profiles of tablets under test are compared to reference tablets. A second case study involves statistically designed mixture experiments used in optimization tablet formulation. Python and JMP features are used to demonstrate the methods used in the two case studies. [ABSTRACT FROM AUTHOR]

In this paper, we establish a common fixed point theorem for two multivalued mappings satisfying some dominated conditions on a complete metric space. This new rational type contractive inequality refines various results in the literature. The main theorem is illustrated with examples. As application, we found the existence of solutions of system nonlinear integral equations and functional equations. [ABSTRACT FROM AUTHOR]

This document is an editorial from the journal "Applications of Mathematics." It discusses the Multiple Scale Systems and Systems with Hysteresis conference that took place in Ostravice, Czech Republic in May 2022. The conference was originally planned for 2020 but was postponed due to the pandemic. The editorial highlights the contributions of Mark Aleksandrovich Krasnosel¿skii and Alexei Pokrovskii to the field of hysteresis and the mathematical theory of systems with hysteresis. It also mentions the development of the MURPHYS conference series, which explores the links between multi-rate systems and hysteresis operators. The editorial concludes by stating that the conference continued the tradition of multidisciplinary MURPHYS meetings and that the conference papers will be of interest to readers of the journal. [Extracted from the article]

The special issue of "Mathematical Methods in the Applied Sciences" is dedicated to Professor Xianling Fan on his 80th birthday, recognizing his significant contributions to Variable Exponent Analysis and Partial Differential Equations with non‐standard growth. Professor Fan, originally from Anyang, Henan Province, China, has had a distinguished career in mathematics, serving in various leadership roles and conducting international academic research. His work has been widely recognized, with numerous publications and awards, highlighting his impact on the field of nonlinear functional analysis. The collection of papers in this special issue celebrates Professor Fan's legacy and contributions to the mathematical community. [Extracted from the article]

Haim Brezis, a renowned mathematician, passed away in July 2024. He made significant contributions to functional analysis and nonlinear partial differential equations. His early work focused on monotone operators and variational equations, providing a framework for optimal transport theory and pedestrian dynamics. In the 1980s, he studied elliptic equations and critical levels of energy, which proved crucial for solving problems in surfaces with constant mean curvature and harmonic maps. Brezis also made important discoveries in the calculus of variations, including a relation between pointwise convergence of functions and convergence of functionals. In the 1990s, he studied the Ginzburg-Landau equations related to superconductivity and superfluidity. He also explored function spaces, Sobolev spaces, and mappings between manifolds, achieving definitive results and making unexpected applications in data analysis and computer science. Brezis was dedicated to education and research dissemination, teaching popular courses and writing influential books. He supervised numerous theses and received numerous awards and honorary degrees. His scientific legacy will continue to inspire researchers worldwide. [Extracted from the article]

This article outlines the necessary requirements for a coupled system of fractional order boundary value involving the Caputo fractional derivative, including its existence, uniqueness, and various forms of Ulam stability. We demonstrate the existence and uniqueness of the proposed coupled system by using the cone-type Leray–Schauder result and the Banach contraction principle. Based on the traditional method of nonlinear functional analysis, the stability is examined. An example is used to provide a clear illustration of our main results. [ABSTRACT FROM AUTHOR]

SARS-CoV-2 and its variants have been investigated using a variety of mathematical models. In contrast to multi-strain models, SARS-CoV-2 models exhibit a memory effect that is often overlooked and more realistic. Atangana-Baleanu's fractional-order operator is discussed in this manuscript for the analysis of the transmission dynamics of SARS-CoV-2. We investigated the transmission mechanism of the SARS-CoV-2 virus using the non-local Atangana-Baleanu fractional-order approach taking into account the different phases of infection and transmission routes. Using conventional ordinary derivative operators, our first step will be to develop a model for the proposed study. As part of the extension, we will incorporate fractional order derivatives into the model where the used operator is the fractional order operator of order Ψ 1 . Additionally, some basic aspects of the proposed model are examined in addition to calculating the reproduction number and determining the possible equilibrium. Stability analysis of the model is conducted to determine the necessary equilibrium conditions as they are also required in developing a numerical setup. Utilizing the theory of nonlinear functional analysis, for the model, Ulam-Hyers' stability is established. We present a numerical scheme based on Newton's polynomial in order to set up an iterative algorithm for the proposed ABC system. The application of this scheme to a variety of values of Φ 1 indicates that there is a relationship between infection dynamics and the derivative's order. We present further simulations which demonstrate the importance and cruciality of different parameters, as well as their effect on the dynamics and administer the disease. Furthermore, this study will provide a better understanding of the mechanisms underlying contagious diseases, thus supporting the development of policies to control them. [ABSTRACT FROM AUTHOR]

In this paper, we present a new extension of Banach-Caristi type theorem for multivalued mappings. We show that our result is not a consequence of multivalued version of Banach contraction principle due to Nadler. We provide an application of our result to the solution of functional equations. [ABSTRACT FROM AUTHOR]

This paper introduces some numerical algorithms for finding solutions of nonlinear problems like functional equations, split feasibility problems (SFPs) and variational inequality problems (VIPs) in the setting of Hilbert and Banach spaces. Our approach is based on the Thakur-Thakur-Postolache (TTP) iterative algorithm and the class of mean nonexpansive mappings. First we provide some convergence results (including weak and strong convergence) in the setting of Banach space. To support these results, we provide a numerical example and prove that our TTP algorithm in this case converges faster to fixed point compared to other iterative algorithms of the literature. After that, we consider two new TTP type projection iterative algorithms to solve SFPs and VIPs on the Hilbert space setting. Our result are new in analysis and suggest new type effective numerical algorithms for finding approximate solutions of some nonlinear problems. [ABSTRACT FROM AUTHOR]

We provide streamlined criteria for evaluating the oscillatory behavior of solutions to a class of higher-order functional differential equations in the non-canonical case. We use a comparison approach with first-order equations that have standard oscillation criteria. Normally, in the non-canonical situation, the oscillation test requires three independent conditions, but we provide criteria with two-conditions without checking the additional conditions. Lastly, we give examples to highlight the significance of the findings. [ABSTRACT FROM AUTHOR]

This paper discusses a hybrid grey wolf optimizer utilizing a clone selection algorithm (pGWO-CSA) to overcome the disadvantages of a standard grey wolf optimizer (GWO), such as slow convergence speed, low accuracy in the single-peak function, and easily falling into local optimum in the multi-peak function and complex problems. The modifications of the proposed pGWO-CSA could be classified into the following three aspects. Firstly, a nonlinear function is used instead of a linear function for adjusting the iterative attenuation of the convergence factor to balance exploitation and exploration automatically. Then, an optimal α wolf is designed which will not be affected by the wolves β and δ with poor fitness in the position updating strategy; the second-best β wolf is designed, which will be affected by the low fitness value of the δ wolf. Finally, the cloning and super-mutation of the clonal selection algorithm (CSA) are introduced into GWO to enhance the ability to jump out of the local optimum. In the experimental part, 15 benchmark functions are selected to perform the function optimization tasks to reveal the performance of pGWO-CSA further. Due to the statistical analysis of the obtained experimental data, the pGWO-CSA is superior to these classical swarm intelligence algorithms, GWO, and related variants. Furthermore, in order to verify the applicability of the algorithm, it was applied to the robot path-planning problem and obtained excellent results. [ABSTRACT FROM AUTHOR]

In this paper we provide sufficient conditions for the existence as well as the uniqueness of solution of general nonlinear functional differential equations, Our results will be obtained using suitable fixed point theorems, We give also some remarks about uniqueness theorem due to Dhage. [ABSTRACT FROM AUTHOR]

In this paper, the model for bovine babesiosis epidemic transmission is analyzed using a fractional operator with a Mittag-Leffler kernel. The existence and uniqueness of the solution of the considered model is studied using real analysis. The Hyers–Ulam (HU) stability is investigated with the help of nonlinear functional analysis. The numerical results of the proposed model are deduced through the Adams–Bashforth technique, which is based on the two-step Lagrangian interpolation method. All results are simulated for a few fractional orders to observe the dynamics of the proposed model. [ABSTRACT FROM AUTHOR]

This paper considers the novel fractional-order operator developed by Atangana-Baleanu for transmission dynamics of the SARS-CoV-2 epidemic. Assuming the importance of the non-local Atangana-Baleanu fractional-order approach, the transmission mechanism of SARS-CoV-2 has been investigated while taking into account different phases of infection and various transmission routes of the disease. To conduct the proposed study, first of all, we shall formulate the model by using the classical operator of ordinary derivatives. We utilize the fractional order derivative and the model will be extended to a model containing fractional order derivatives. The operator being used is the fractional differential operator and has fractional order Φ 1 . The model is analyzed further and some basic aspects of the model are investigated besides calculating the basic reproduction number and the possible equilibria of the proposed model. The equilibria of the model are examined for stability purposes and necessary conditions for stability are obtained. Stability is also necessary in terms of numerical setup. The theory of non-linear functional analysis is employed and Ulam-Hyers's stability of the model is presented. The approach of newton's polynomial is considered and a new numerical scheme is developed which helped in presenting an iterative process for the proposed ABC system. Based on this scheme, sample curves are obtained for various values of Φ 1 and a pattern is derived between the dynamics of the infection and the order of the derivative. Further simulations are presented which show the cruciality and importance of various parameters and the impact of such parameters on the dynamics and control of the disease is presented. The findings of this study will also provide strong conceptual insights into the mechanisms of contagious diseases, assisting global professionals in developing control policies. [ABSTRACT FROM AUTHOR]

The existence, uniqueness, and various forms of Ulam–Hyers (UH)-type stability results for nonlocal pantograph equations are developed and extended in this study within the frame of novel p s i -piecewise Caputo fractional derivatives, which generalize the piecewise operators recently presented in the literature. The required results are proven using Banach's contraction mapping and Krasnoselskii's fixed-point theorem. Additionally, results pertaining to UH stability are obtained using traditional procedures of nonlinear functional analysis. Additionally, in light of our current findings, a more general challenge for the pantograph system is presented that includes problems similar to the one considered. We provide a pertinent example as an application to support the theoretical findings. [ABSTRACT FROM AUTHOR]

An accurate nonlinear buckling analysis of functional graded multilayer GPL‐Fiber reinforced hybrid composites (FG multilayer GPL‐Fiber RHCs) cylindrical shells under hygro‐thermo‐mechanical loadings is performed. The axisymmetric pre‐buckling effect, which is usually neglected in the classical eigen‐buckling analysis, is considered to improve the accuracy of critical buckling loads. Nonlinear governing equations are derived by adopting the high‐order shear deformation theory and Novozhilov's nonlinear shell theory. Accurate critical buckling loads and explicit buckling mode shapes are obtained by the Galerkin method. Comparisons with results of existing literature are presented to validate the accuracy of present solutions. A comprehensive parametric study of key influencing parameters on the structural stability of the FG multilayer GPL‐Fiber RHCs cylindrical shell is investigated in detail. The numerical results indicate that the stability of such shell highly depends on the temperature rise and moisture absorption, and contents and distribution profiles of GPLs and fibers could be optimized to enhance the anti‐buckling performance of the shell. [ABSTRACT FROM AUTHOR]