Manuel De la Sen

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Verified

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• PhD
• Emeritus Professor at University of the Basque Country

The main objective of this paper is to find the sufficient conditions for the existence of best proximity points for multivalued non-self mapping in the setting of O-complete metric space. We prove the existence of best proximity point by introducing the new concept called proximal relation in O-sets along with various contraction conditions on mul...

In this paper, we study generalized (C)-conditions, specifically the Kannan-Suzuki-(C) condition (abbreviated as the (KSC)-condition). We employ the M-iteration process to investigate the convergence behavior of map-pings satisfying the KSC-condition and demonstrate that this approach offers improved convergence speed and computational efficiency c...

This paper studies the boundedness and convergence properties of the sequences generated by strict and weak contractions in metric spaces, as well as their fixed points, in the event that finite jumps can take place from the left to the right limits of the successive values of the generated sequences. An application is devoted to the stabilization...

We aimed to analyze a new class of sequential fractional differential inclusions that involves a combination of ς-Hilfer and ς-Caputo fractional derivative operators, along with non-separated boundary conditions. Two cases of convex-valued and non-convex-valued set-valued maps are considered. Our outcomes are obtained from some famous theorems of f...

In this study, we investigate systems known as nonlinear fractional delay differential (nLFDD) systems, characterized by finite state delays and fractional orders within the range of 0\lt \eta \le 1\lt \zeta \le 2 , situated infinite-dimensional settings. We utilize the controllability Gramian matrix to establish both necessary and sufficient condi...

This paper investigates the existence of common attractors for generalized θ-Hutchinson operators within the framework of partial metric spaces. Utilizing a finite iterated function system composed of θ-contractive mappings, we establish theoretical results on common attractors, generalizing numerous existing results in the literature. Additionally...

The transmission rate (β(t)) plays a crucial role in disease spread, making its measurement essential for effective control. However, existing techniques for its estimation are impractical as they rely on typically unavailable data. To address this, a prior analysis of the most frequently reported data during the Coronavirus Disease 2019 (COVID-19)...

This paper formalizes the analytic expressions and some properties of the evolution operator that generates the state-trajectory of dynamical systems combining delay-free dynamics with a set of discrete, or point, constant (and not necessarily commensurate) delays, where the parameterizations of both the delay-free and the delayed parts can undergo...

In this paper, we use Petryshyn’s fixed point (FP) theorem to investigate the existence of solutions to a system of nonlinear fractional integral equations (FIEs) in the context of real Banach spaces (BSs). Also, the method of measuring non-compactness (MNC) is the main tool used in the analysis of the product of three compounds. Many previous theo...

This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana-Baleanu-Caputo (ABC) derivative, we transform the system into an equivalent fixed-point...

This paper studies the properties of the evolution operators of a class of time-delay systems with linear delayed dynamics. The considered delayed dynamics may, in general, be time-varying and associated with a finite set of finite constant point delays. Three evolution operators are defined and characterized. The basic evolution operator is the so...

This paper introduces a novel extension of Caputo-Atangana-Baleanu and Riemann-Atangana-Baleanu fractional derivatives from constant to increasing variable order. We generalize the fractional order from a fixed value in (0, 1] to a time-dependent function in (k, k + 1], where k ≥ 0. The corresponding Atangana-Baleanu fractional integral is also ext...

This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system in the sense that it is subject to p...

Developing a model of fractional differential systems and studying the existence and stability of a solution is considebly one of the most important topics in the field of analysis. Therefore, this manuscript was dedicated to deriving a new type of fractional system that arises from the combination of three sequential fractional derivatives with fr...

This paper deals with the conditions on external positivity of linear time-invariant systems subject to a finite number of constant point delays. The relations and comparisons between the state and output of the whole delayed system with those of its associated delay-free and delay-free dynamics auxiliary systems are investigated. "Ad hoc" versions...

This paper derives some generalized Schur-type stability results of polynomials based on several forms and generalizations of the Eneström–Kakeya theorem combined with the Rouché theorem. It is first investigated, under sufficiency-type conditions, the derivation of the eventually generalized Schur stability sufficient conditions which are not nece...

This article presents the notions of extended b-gauge space ( U , Q φ ; Ω ) \left(U,{Q}_{\varphi ;\Omega }) and extended J φ ; Ω {{\mathcal{J}}}_{\varphi ;\Omega } -families of generalized extended pseudo-b-distances on U U . Furthermore, we look at these extended J φ ; Ω {{\mathcal{J}}}_{\varphi ;\Omega } -families on U U and define the extended J...

The explicit aim of this manuscript is to obtain fixed point consequences under novel ψ-contraction mappings in a complete cone metric space over Banach algebra. We connect and relate different fixed point theorems by using the idea of ψ-contraction mappings, providing a thorough viewpoint that deepens our comprehension of this topic. Our theorems...

This present work develops a nonlinear SIRS fractional-order model with a system of four equations in the Caputo sense. This study examines the impact of positive and negative attitudes towards vaccination, as well as the role of government actions, social behavior and public reaction on the spread of infectious diseases. The local stability of the...

Some boundedness and convergence properties of generalized Fibonacci’s-type recurrences and their associated iterated recurrence ratios between pairs of consecutive terms are discussed under a wide number of initial conditions. Also, a more general, so-called k,q Fibonacci’s recurrence and the associated Fibonacci’s ratio recurrences are investigat...

The vital goals of this manuscript are to combine metric-like spaces with S−metric spaces under a control function to obtain a new space called the controlled S−metric-like spaces (CSMLSs, for short). Under this name, many fixed-point (FP) results have been obtained for multi-valued mappings (MVMs). In addition, we present several non-trivial examp...

This paper investigates sufficiency-type conditions for strictly decreasing solutions of linear time-delay differential systems subject to a finite number of time-varying bounded point delays. The delay functions are not required to be time-differentiable nor even continuous but simply piecewise bounded continuous. It is not also required for the d...

Many scholars have lately explored fractional-order boundary value issues with a variety of conditions, including classical, nonlocal, multipoint, periodic/anti-periodic, fractional-order, and integral boundary conditions. In this manuscript, the existence and uniqueness of solutions to sequential fractional differential inclusions via a novel set...

In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and discuss the language of k-forcing automata for particular graphs. Also, for some graphs w...

This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynami...

This manuscript is devoted to ensuring the existence of a solution to nonlinear fractional integral equations with three variables under a measure of noncompactness. In order to accomplish our main goal, we develop a new fixed point theorem that generalizes Darbo's fixed point theorem by utilizing a measure of noncompactness and a new contraction o...

In this paper, we present a new four-step iterative scheme namely DH-iterative which is faster than many super algorithms in the literature for numerical reckoning fixed points. Under this algorithm, some fixed point convergence results and ω 2-stability for contractive-like and Reich-Suzuki-type nonexpansive mappings are proposed. Our results exte...

Atomic Localization by Damping Spectrum of Surface Plasmon Polariton Waves(Gold)

In this paper, we present tripling fixed point results for extended contractive mappings in the context of a generalized metric space. Many publications in the literature are improved, unified, and generalized by our theoretical results. Furthermore, the Ulam-Hyers stability problem for the tripled fixed point problem in vector-valued metric spaces...

Among other things, finding solutions for functional as well as other types of problems (including differential and integral) by suggesting fixed-point procedures is a difficult task, especially when we study the approximation techniques in the absence of linearity in the domain of definition. In this paper, an effective iterative approximation pro...

The COVID-19 outbreak has brought to the forefront the importance of predicting and controlling an epidemic outbreak with policies such as vaccination or reducing social contacts. This paper studies an SIHR epidemic model characterized by susceptible (S), non-seriously infected (I), hospitalized (H), and recovered (R) subpopulations, and dynamic va...

In this manuscript, we introduce a new notion of generalized parametric bipolar metric space as a generalization of generalized parametric space and bipolar metric space. We also introduce Boyd-Wong type contractions for covariant and contravariant mappings to prove the fixed point results in the newly defined space. Some examples are also provided...

In the present study, we commenced by presenting a new class of maps, termed noncyclic $ (\varphi, \mathcal{R}^t) $-enriched quasi-contractions within metric spaces equipped with a transitive relation $ \mathcal{R}^t $. Subsequently, we identified the conditions for the existence of an optimal pair of fixed points pertaining to these mappings, ther...

We introduce the class of $ \psi $-convex functions $ f:[0, \infty)\to \mathbb{R} $, where $ \psi\in C([0, 1]) $ satisfies $ \psi\geq 0 $ and $ \psi(0)\neq \psi(1) $. This class includes several types of convex functions introduced in previous works. We first study some properties of such functions. Next, we establish a double Hermite-Hadamard-type...

We unified several kinds of convexity by introducing the class $ \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ of $ (\zeta, w) $-admissible functions $ F: [0, 1]\times I\times I\to \mathbb{R} $. Namely, we proved that most types of convexity from the literature generate functions $ F\in \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ for some $ \zeta\in C(...

We consider the class of functions $ u\in C^2((0, \infty)) $ satisfying second-order differential inequalities in the form $ u''(x)+\frac{k}{x^2}u(x)\geq 0 $ for all $ x > 0 $. For this class of functions, we establish Hermite-Hadamard-type inequalities in both cases ($ k=\frac{1}{4} $ and $ 0 < k < \frac{1}{4} $). We next extend our obtained resul...

In this paper, we are concerned with the study of the existence and uniqueness of fixed points for the class of functions $ f: C\to C $ satisfying the inequality \begin{document}$ \ell\left(\alpha f(t)+(1-\alpha)f(s)\right)\leq \sigma \ell(\alpha t+(1-\alpha)s) $\end{document} for every $ t, s\in C $ with $ f(t)\neq f(s) $, where $ C $ is a closed...

In this article, the probabilistic metric distance between two disjoint sets is utilised to define the essential criteria for the existence and uniqueness of the best proximity point, which takes into account the global optimization problem. In order to solve this problem, we pretend that we are trying to obtain the optimal approximation to the sol...

In this study, we examine the plant–herbivore discrete model of apple twig borer and grape vine interaction, with a particular emphasis on the extended weak-predator response to Holling type-II response. We explore the dynamical and qualitative analysis of this model and investigate the conditions for stability and bifurcation. Our study demonstrat...

Fins are extended surfaces that increase the surface area for heat transfer between a hot source and an ambient fluid. Heat transfer is increased by adding radial or concentric annular fins to the outside surface of a circular conduit. The fins are used in devices that exchange heat such as car radiators, electrical equipment, and heat exchangers....

The objective of this research is to establish new results for set-valued dominated mappings that meet the criteria of advanced locally contractions in a complete extended-metric space. Additionally, we intend to establish new fixed point outcomes for a couple of dominated multi-functions on a closed ball that satisfy generalized local contractions...

Two time-varying Beverton–Holt models are investigated in which the population of the same species evolves jointly in two coupled habitats which can be subject to population exchanges. Both habitats can have different parameterizations concerning their intrinsic growth rates and their environment carrying capacities due to different environmental c...

The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. In addition, we examine the stability of fixed-point sets for...

This note generalizes several existing results related to Hermite–Hadamard inequality using h-Godunova–Levin and (h1,h2)-convex functions using a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. This study uses a non-singular kernel and constructs some new theorems associated with fractional order integrals. F...

In this manuscript, we prove the existence and uniqueness of a common best proximity point for a pair of non-self mappings satisfying the iterative mappings in a complete fuzzy multiplicative metric space. We consider the pair of non-self mappings $ X:\mathcal{P}\rightarrow \mathcal{G} $ and $ Z:\mathcal{P }\rightarrow \mathcal{G} $ and the mapping...

This study aims to investigate the refining relation between two vector general fuzzy automata (VGFA) and prove that refining relation is an equivalence relation. Moreover, Also, we prove that if there exists a refining equivalence between two VGFA, then they have the same language. After that, by considering the notion of refining equivalence, we...

In this article, a class of cyclic (noncyclic) operators are defined on Banach spaces via concept of measure of noncompactness using some abstract functions. The best proximity point (pair) results are manifested for the said operators. The obtained main results are applied to demonstrate the existence of optimum solutions of a system of fractional...

In this work, we prove the existence of the best proximity point results for ⊥-contraction (orthogonal-contraction) mappings on an O-complete metric space (orthogonal-complete metric space). Subsequently, these existence results are employed to establish the common best proximity point result. Finally, we provide suitable examples to demonstrate th...

This study demonstrates that, for the non-linear contractive conditions in Neutrosophic metric spaces, a common fixed-point theorem may be proved without requiring the continuity of any mappings. A novel commutativity requirement for mappings weaker than the compatibility of mappings is used to demonstrate the conclusion. We provide several example...

This paper investigates the asymptotic hyperstability of a single-input–single-output closed-loop system whose controlled plant is time-invariant and possesses a strongly strictly positive real transfer function that is subject to internal and external point delays. There are, in general, two controls involved, namely, the internal one that stabili...

In this article, we introduce the concept of multivalued fractals in neutrosophic metric spaces using an iterated multifunction system made up of a finite number of neutrosophic B-contractions and neutrosophic Edelstein contractions. Further, we show that multivalued fractals exist and are unique in both complete neutrosophic metric spaces and comp...

The objective of the manuscript is to build coupled singular fractional-order differential equations with time delay. To study the underline problem, an integral representation is initially discussed and the operator form of the solution is investigated using various supplementary hypotheses. Also, the existence and uniqueness of the considered pro...

This paper considers a more general eventually time-varying Beverton-Holt equation for species evolution which can include a harvesting action and a penalty for overpopulation numbers. The harvesting action may be positive (typically consisting of hunting or fshing) or negative which refers to repopulation within the environment. One considers also...

This article explores the stability of involution in fuzzy C★-algebras through the use of a functional inequality. We present an approach to obtaining an approximate involution in fuzzy C★-algebras by utilizing a fixed-point method. Moreover, for greater clarity, we implemented Python code for the main theorem.

In a recent paper, Khojasteh et al. presented a new collection of simulation functions, said Z-contraction. This form of contraction generalizes the Banach contraction and makes different types of nonlinear contractions. In this article, we discuss a pair of nonlinear operators that applies to a nonlinear contraction including a simulation function...

We study some common results in C*-algebra-valued Sb-metric spaces. We also present an interesting application of an existing and unique result for one type of integral equation.

In this paper, we introduce the concept of fuzzy-controlled bipolar metric space and prove some fixed-point theorems in this space. Our results generalize and expand some of the literature’s well-known results. We also provide some applications of our main results to integral equations.

Symmetry can play an important role in the study of boundary value problems, which are a type of problem in mathematics that involves finding the solutions to differential equations subject to given boundary conditions. Integral transforms play a crucial role in solving ordinary differential equations (ODEs), partial differential equations (PDEs),...

In this study, we analyzed the inertia effect on the axisymmetric squeeze flow of slightly viscoelastic fluid film between two disks. A system of nonlinear partial differential equations (PDEs) in cylindrical coordinates, along with nonhomogenous boundary conditions, illustrates the phenomenon of fluid flow caused by squeezing with the inertia effe...

There is significant interaction between the class of symmetric functions and other types of functions. The multiplicative convex function class, which is intimately related to the idea of symmetry, is one of them. In this paper, we obtain some new generalized multiplicative fractional Hermite–Hadamard type inequalities for multiplicative convex fu...

This paper aims to study the convergence of Picard’s iteration to a best proximity pair for a class of noncyclic mappings with the help of projections in hyperbolic uniformly convex metric spaces. Some sufficient conditions are provided to guarantee the existence of a common best proximity pair for a pair of noncyclic mappings. Moreover, the existe...

This paper presents the dynamical aspects of a nonlinear multi-term pantograph-type system of fractional order. Pantograph equations are special differential equations with proportional delays that are employed in many scientific disciplines. The pantograph mechanism, for instance, has been applied in numerous scientific disciplines like electrodyn...

In this study, we utilize the direct method (Hyers approach) to examine the refined stability of the additive, quartic, and sextic functional equations in modular spaces with and without the $ \Delta _{2} $-condition. We also use the direct approach to discuss the Ulam stability in $ 2 $-Banach spaces. Ultimately, we ensure that stability of above...

In this article, a new deterministic disease system is constructed to study the influence of treatment adherence as well as awareness on the spread of tuberculosis (TB). The suggested model is composed of six various classes, whose dynamics are discussed in the sense of the Caputo fractional operator. Firstly the model existence of a solution along...

In this manuscript, a novel general class of contractions, called Jaggi–Suzuki-type hybrid (G-α-ϕ)-contraction, is introduced and some fixed point theorems that cannot be deduced from their akin in metric spaces are proved. The dominance of this family of contractions is that its contractive inequality can be specialized in various manners, dependi...

In this paper, at first, we define the notion of general fuzzy automaton over a field; we call this automaton vector general fuzzy automaton (VGFA). Moreover, we present the concept of max-min vector general fuzzy automaton. We show that if two max-min VGFA are similar, they constitute an isomorphism. After that, we prove that if two VGFA constitut...

In this study, we consider the stochastic Konno–Oono system to investigate the soliton solutions under the multiplicative sense. The multiplicative noise is considered firstly in the Stratonovich sense and secondly in the Ito^ sense. Applications of the Konno–Oono system include current-fed strings interacting with an external magnetic field. The F...

The aim of this study is to provide a generalization of prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing vague weakly complete Γ-ideals of commutative Γ-rings. A novel algebraic structure of a primary vague Γ-ideal of a commutative Γ-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-s...

The entirety of the information regarding a subatomic particle is encoded in a wave function. Solving quantum mechanical models (QMMs) means finding the quantum mechanical wave function. Therefore, great attention has been paid to finding solutions for QMMs. In this study, a novel algorithm that combines the conformable Shehu transform and the Adom...

The objective of this work was to investigate the dynamics of host–parasitoid model with spatial refuge effect. For this, two discrete host–parasitoid models were considered under spatial refuge effect. Suppose that a constant population of hosts may seek refuge and protection from an attack of parasitoids. We found the parametric factors affecting...

The purpose of this paper is to present some fixed point approaches for multi-valued Prešić k-step iterative-type mappings on a metric space. Furthermore, some corollaries are obtained to unify and extend many symmetrical results in the literature. Moreover, two examples are provided to support the main result. Ultimately, as potential applications...

The goal of this work is to study the existence of a unique solution and the Ulam-Hyers stability of a coupled system of generalized hybrid pantograph equations with fractional deformable derivatives. Our main tool is Banach's contraction principle. The paper ends with an example to support our results.

This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractio...

In this paper, a general framework for the fractional boundary value problems is presented. The problem is created by Riemann-Liouville type two-term fractional differential equations with a fractional bi-order setup. Moreover, the boundary conditions of the suggested system are considered as mixed Riemann-Liouville integro-derivative conditions wi...

Recent progresses in nanotechnologies and nanoscience have led to the creation of hybrid nanofluids, which are a complicated category of fluids with superior thermal features to regular nanofluids. The current framework demonstrates the importance of a two-dimensional steady incompressible axisymmetric flow of Maxwell hybrid nanofluid over double d...

In this paper, we present some generalized multi-valued contraction results on cone metric spaces. We use some maximum and sum types of contractions for a pair of multi-valued mappings to prove some common fixed point theorems on cone metric spaces without the condition of normality. We present an illustrative example for multi-valued contraction m...

Recent progresses in nanotechnologies and nanoscience have led to the creation of hybrid nano-fluids, which are a complicated category of fluids with superior thermal features to regular nano-fluids. The current framework demonstrates the importance of a two-dimensional steady incompressible axisymmetric flow of Maxwell hybrid nanofluid over double...

Cancer is dangerous and one of the major diseases affecting normal human life. In this paper, a fractional-order cancer model with stem cells and chemotherapy is analyzed to check the effects of infection in individuals. The model is investigated by the Sumudu transform and a very effective numerical method. The positivity of solutions with the ABC...

This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry and convexity increases its significance. In this paper, we first establish an identity that is crucial in investigating fractional mean inequalities. Then, we establish the main results involvin...

Despite the existence of a secure and reliable immunization, measles, also known as rubeola, continues to be a leading cause of fatalities globally, especially in underdeveloped nations. For investigation and observation of the dynamical transmission of the disease with the influence of vaccination, we proposed a novel fractional order measles mode...

There has been a long-lasting impact of the lockdown imposed due to COVID-19 on several fronts. One such front is climate which has seen several implications. The consequences of climate change owing to this lockdown need to be explored taking into consideration various climatic indicators. Further impact on a local and global level would help the...

The goal of this paper is to present a new class of contraction mappings, so-called $ \eta _{\theta }^{\ell } $-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for $ \eta _{\theta }^{\ell } $-contraction mappings are introduced. Furthermore, to support our results, two examples are provided. F...

This paper presents the modeling and stabilization of a floating offshore wind turbine (FOWT) using oscillating water columns (OWCs) as active structural control. The novel concept of this work is to design a new FOWT platform using the ITI Energy barge with incorporated OWCs at opposite sides of the tower, in order to alleviate the unwanted system...

We investigate cylindrical and spherical solitons in electron-ion (EI) plasma that contains hot (cold) electrons with stationary ions. The magneto-hydrodynamic equations are solved with the aid of the reductive perturbation (RP) technique, leading to the modified Korteweg–De Vries (mKdV) equation for the non-linear behaviour of the solitary waves i...

Potential in a Streaming Electron-Ion Magnetoplasma: Phase Plane Analysis. Symmetry 2023, 15, 436. https:// Abstract: We investigate cylindrical and spherical solitons in electron-ion (EI) plasma that contains hot (cold) electrons with stationary ions. The magneto-hydrodynamic equations are solved with the aid of the reductive perturbation (RP) tec...