Jorge E. Macías-Díaz

Autonomous University of Aguascalientes | UAA · Departamento de Matemáticas y Física

In this article, we study the fractional form of a well-known dynamical system from mathematical biology, namely, the Lotka–Volterra model. This mathematical model describes the dynamics of a predator and a prey, and we consider here the fractional form using the Rabotnov fractional-exponential (RFE) kernel. In this work, we derive an approximate f...

This paper reviews the application of Artificial Neural Network (ANN) models to time series prediction tasks. We begin by briefly introducing some basic concepts and terms related to time series analysis, and by outlining some of the most popular ANN architectures considered in the literature for time series forecasting purposes: Feed Forward Neura...

This work investigates the quadratic and quartic nonlinear diffusion-reaction equations with nonlinear convective flux terms, which are investigated analytically. Diffusion-reaction equations have a wide range of applications in several scientific areas, such as chemistry, biology, and population dynamics of the species. The new extended direct alg...

In this study, a generalization of the Estevez–Mansfield–Clarkson equation which considers the presence of conformable time-fractional derivatives is investigated analytically. The integer-order model finds applications in mathematical physics, optics and the investigation of shape developing in liquid drops. In the present manuscript, the Sardar s...

This manuscript establishes the theoretical numerical features of a finite-difference scheme that conserves the dissipation of Gibbs' free energy for a nonlinear multidimensional combustion equation. Our system considers fractional derivatives of the Caputo class in the temporal variable, along with Riesz fractional operators in the spatial coordin...

We study a fractional model for tumor growth and derive its general solution, the blow-up time and the radius of convergence. The model is simplified then to fit human data. The results show that there is a noticeable variation in the value of the scaling exponent depending on whether the model is fractional or integer. This supports the idea that...

Soliton solutions of a (2 + 1)-dimensional reaction-diffusion problem are derived in the present work using the generalized Riccati equation mapping method. The model captures the time evaluation of disturbance and addresses modeling real-world phenomena such as turbulence, traffic flow, heat and fluid transport, and gas dynamics. To start with, th...

This manuscript reports on a nonlocal mathematical system to model the spreading of polio among a community of human individuals. Our model consists of four compartments: susceptible, exposed, infected and vaccinated individuals. The mathematical model considers spatial diffusion, and temporal fractional derivatives of the Caputo type. We use non-n...

Efficient mapping algorithms have been implemented in different fields of robotics applications. Some of those applications are in the mapping of environments with difficult accessibility, the planning of service or emergency assistant robots, or as supporting tools in helping people with disabilities. In those examples, the essential task of a map...

In this work, we extend the Zakharov-Rubenchik system to the fractional case by using Riesz operators of fractional order in space. We prove that the system is capable of preserving extensions of the mass, energy, momentum and two linear functionals. In a second stage, we propose a discretization to approximate the solutions of our model. In the wa...

In the present work, we explored the dynamics of single kinks, kink–anti-kink pairs and bound states in the prototypical fractional Klein–Gordon example of the sine-Gordon equation. In particular, we modified the order β of the temporal derivative to that of a Caputo fractional type and found that, for 1<β<2, this imposes a dissipative dynamical be...

Efficient mapping algorithms have been implemented in different fields of robotics applications. Some of those applications are in the mapping of environments with difficult accessibility, the planning of service or emergency assistant robots, or as supporting tools in helping people with disabilities. In those examples, the essential task of a map...

This article investigates the propagation of a deadly human disease, namely, leprosy. To this end, an integer-order system of differential equations is considered. At the outset, the mathematical model is transformed into a fractional-order model by introducing the Caputo differential operator of arbitrary order. A result is established which ensur...

In this work, we investigate particular properties on the completion of symmetric spaces. Symmetric spaces are metric spaces and, naturally, question arises as to whether their completions are also symmetric. In this work, we provide an affirmative response to this question. More precisely, we prove that every metric space is isometrically a subset...

Consider a polynomial P with complex coefficients and nonzero roots. What is the relation between the coefficients of P , and those of the polynomial P whose roots are reciprocal of the roots of P ? Is it possible to express the coefficients of P through a formula which depends on the coefficients of P ? The purpose of this note is to revisit this...

The present work reports on a device for the processing of electric signals and the physical interpretation of the outputs. The aim is to execute actions through external devices by analyzing the bioelectric signals from the human eye or electrooculograms (EOGs). More concretely, an EOG digital controller to work as assistive technology for motor d...

In this work, a simple strategy for iteratively applying Leibniz's integration rule from elementary calculus to operational problems was evaluated. Leibniz's integration rule (also known as the "integration by parts formula") is a relatively simple formula. However, some typical antiderivative calculus problems require applying this formula iterati...

The integration of internationally sustainable practices into supply chain management methodologies is known as "green supply chain management." Reducing the supply chain's overall environmental impact is the main objective in order to improve corporate connections and the social, ecological, and economic ties with other nations. In order to accomp...

The concept of convexity is fundamental in order to produce various types of inequalities. 16 Thus, convexity and integral inequality are closely related. The objectives of this paper are to present 17 a new class of up and down convex fuzzy-number valued functions known as up and down expo-18 nential trigonometric convex fuzzy-number valued mappin...

In this work, we extend the Rosenau-Kawahara equation (RKE) to the fractional scenario by using space-fractional operators of the Riesz kind. We prove that this system has functional quantities similar to the energy and the mass of the integer-order model, and we show that they are conserved. A discretized form of the model is proposed along with d...

In the present manuscript, we depart from a two-dimensional form of a nonlinear system from fluid dynamics, consisting of two partial differential equations with two unknown functions, one of them is complex-valued and the other real-valued. This model possesses four conserved quantities, namely, the mass, the energy and two momenta. In a first sta...

Esta monografía está dirigida a estudiantes de posgrado e investigadores. Para su comprensión, es necesario contar con bases sólidas sobre conjuntos, grupos, anillos, categorías y topología. Como todos los trabajos de László Fuchs, la exposición de los temas en este libro es sistemática, coherente, concisa, creativa y elegante. Varios resultados se...

This study explores the application of generalized conformable derivatives in modeling hotel demand dynamics in Mexico using the Gompertz-type model. The research focuses on customizing conformable functions to fit the unique characteristics of the Mexican hotel industry, considering the Tourist Area Life Cycle (TALC) model, aiming to enhance forec...

In this work, we present a numerical scheme of the Higgs Boson equation in De Sitter space. One of its main characteristics is its variational form, which translates into the modeling of the energy associated with the continuous case. The equation shown in this work is a generalization that contemplates a potential and a time-dependent diffusion co...

Many fields of mathematics rely on convexity and nonconvexity, especially when stud-16 ying optimization issues, where it stands out for a variety of practical aspects. Due to the behaviour 17 of its definition, the idea of convexity also contributes significantly to the discussion of inequalities. 18 The concepts of symmetry and convexity are rela...

n this study, we provide an efficient simulation to investigate the behavior of the solution of the Brusselator system, a biodynamic system, using the Rabotnov fractional-exponential (RFE) kernel fractional derivative. An equation system of fractional differential equations can be used to represent this model. The fractional-order derivative of a p...

In this work, we present a system composed of three identical Duffing oscillators coupled bidirectionally. Starting from a Lagrangian that describes the system, an integral of motion is obtained by means of Noether's theorem. The dynamics of the model is studied using bifurcation diagrams, Lyapunov exponents, time-series analysis, phase spaces, Poi...

Several academic and budgetary applications in robotics use low-cost encoders which usually present errors inherent to the fabrication of their components or the surrounding environment. However, the data gathered from these sensors could be used successfully if the estimations based on the data are be compensated. This note presents an efficient m...

Modern imaging strategies are paramount to studying living systems such as cells, bacteria, and fungi and their response to pathogens, toxicants, and nanomaterials (NMs) as modulated by exposure and environmental factors. The need to understand the processes and mechanisms of damage, healing, and cell survivability of living systems continues to mo...

In this work, a master-slave system composed by a pair of damped Duffing oscillators with variable coefficients and nonlinear coupling is investigated. An integral of motion for the system is obtained {using a symmetry transformation and Noether's theorem.} Some numerical examples are presented for different cases of damping and oscillation frequen...

In this research, a generalization of Verhulst’s equation is proposed, to establish a model of fungus growth, the Caputo time-fractional derivative is used to that end. The main property of the logistics function is an asymptotic equilibrium point, it is verified that this generalization also accomplishes this state. With the help of a fixed-point...

In the present work we explore the dynamics of single kinks, kink-anti-kink pairs and bound states in the prototypical fractional Klein-Gordon example of the sine-Gordon equation. In particular, we modify the order $\beta$ of the temporal derivative to that of a Caputo fractional type and find that, for $1<\beta<2$, this imposes a dissipative dynam...

Mathematical models are crucial for understanding complex biological systems, especially those with intricate behaviors. These models are typically based on coupled linear or nonlinear partial differential equations. In our study, we employ the Laplace Variational Method to investigate the impact of chemotherapy on cancer cells, which are represent...

The purpose of this article is to establish several new forms of Hermite-Hadamard inequalities by utilizing fractional integral operators via a totally interval midpoint-radius order relation for differentiable Godunova-Levin mappings. Moreover, in order to verify our main results, we construct some non-trivial examples and remarks that lead to oth...

The purpose of this article is to establish several new forms of Hermite-Hadamard inequalities by utilizing fractional integral operators via a totally interval midpoint-radius order relation for differentiable Godunova-Levin mappings. Moreover, in order to verify our main results, we construct some non-trivial examples and remarks that lead to oth...

This study examines the effects of various M-shaped water wave shapes on coastal environments for the modified regularized long-wave equation (MRLWE). This work explores the complex dynamics of sediment transport, erosion, and coastal stability influenced by different wave structures using the Hirota bilinear transformation as a basic analytical to...

In honor of the great Russian mathematician A. N. Kolmogorov, we would like to draw attention in the present paper to a curious mathematical observation concerning fractional differential equations describing physical systems, whose time evolution for integer derivatives has a time-honored conservative form. This observation, although known to the...

In honor of the great Russian mathematician A. N. Kolmogorov, we would like to draw attention in the present paper to a curious mathematical observation concerning fractional differential equations describing physical systems, whose time evolution for integer derivatives has a time-honored conservative form. This observation, although known to the...

This work aims at providing a concise review of various agri-food models that employ fractional differential operators. In this context, various mathematical models based on fractional differential equations have been used to describe a wide range of problems in agri-food. As a result of this review, we found out that this new area of research is f...

In this article, a semi-analytical method for effectively solving the time-fractional modified KdV equation, which describes dust acoustic waves in a non-magnetized dust plasma is presented in the Homotopy Analysis Shehu Transform Method (HASTM). Using the Atangana-Balean time-fractional derivative, a powerful tool is employed to methodically inves...

In this article, a generalized form of the Davey–Stewartson system, consisting of three nonlinear coupled partial differential equations, will be studied. The system considers the presence of fractional spatial partial derivatives of the Riesz type, and extensions of the classical mass, energy, and momentum operators will be proposed in the fractio...

In recent years, fractional calculus has witnessed tremendous progress in variousareas of sciences and mathematics [...]

Background and objective: In this work, a mathematical model based on differential equations is proposed to describe the propagation of polio in a human population. The motivating system is a compartmental nonlinear model which is based on the use of ordinary differential equations and four compartments, namely, susceptible, exposed, infected and...

In this work, we introduce generalized Raina fractional integral operators and derive Chebyshev-type inequalities involving these operators. In a first stage, we obtain Chebyshev-type inequalities for one product of functions. Then we extend those results to account for arbitrary products. Also, we establish some inequalities of the Chebyshev type...

Tumor invasion follows a complex mechanism which involves cell migration and proliferation. To study the processes in which primary and secondary metastases invade and damage the normal cells, mathematical models are often extremely useful. In this manuscript, we present a mathematical model of acid-mediated tumor growth consisting of radially symm...

A system of two partial differential equations with fractional diffusion is considered in this study. The system extends the conventional Zakharov system with unknowns being nonlinearly coupled complex- and real-valued functions. The diffusion is understood in the Riesz sense, and suitable initial–boundary conditions are imposed on an open and boun...

Background and objective: In this manuscript, we consider a compartmental model to describe the dynamics of propagation of an infectious disease in a human population. The population considers the presence of susceptible, exposed, asymptomatic and symptomatic infected, quarantined, recovered and vaccinated individuals. In turn, the mathematical mo...

Boundedness is an essential feature of the solutions for various mathematical and numerical models in the natural sciences, especially those systems in which linear or nonlinear preservation or stability features are fundamental. In those cases, boundedness of the solutions outside a set of zero measure is not enough to guarantee that the solutions...

In this manuscript, we present a generalized deformed sum inspired by the non-additive property of entropies such as those investigated by Tsallis and Shannon in the context of information theory. From this deformed sum, we define a generalization of the Vitali set and proved its non-measurability. Moreover, the standard sum is recovered as the def...

A dissipation-preserving numerical scheme is proposed and theoretically analyzed for the first time to solve the Caputo-Riesz time-space-fractional generalized nonlinear Klein-Gordon equation. More concretely, we investigate a multidimensional nonlinear wave equation with generalized potential, involving Caputo temporal fractional derivatives and R...

Science has benefited greatly from the theory of convexity both in pure and applied sciences. The concepts of convexity and integral inequality can be linked in accordance with their definitions. Since the last few years, there has been a growing connection between the two, and we can apply what we learn from one to the other. Utilizing unique and...

In this work, we design and analyze a discrete model to approximate the solutions of a parabolic partial differential equation in multiple dimensions. The mathematical model considers a nonlinear reaction term and a space-dependent diffusion coefficient. The system has a Gibbs' free energy, we establish rigorously that it is non-negative under suit...

The goal of this study is to create new variations of the well-known Hermite-Hadamard inequality (-inequality) for preinvex interval-valued functions (preinvex-s). We develop several additional inequalities for the class of functions whose product is preinvex-s. The findings described here would be generalizations of those found in previous studies...

In this study, an integer-order rabies model is converted into the fractional-order epidemic model. To this end, the Caputo fractional-order derivatives are plugged in place of the classical derivatives. The positivity and boundedness of the fractional-order mathematical model is investigated by applying Laplace transformation and its inversion. To...

The objective of the current paper is to incorporate the new class and concepts of convexity and Hermite-Hadamard inequality with the fuzzy Riemann integral operators because almost all classical single-valued and interval-valued convex functions are special cases of fuzzy-number valued convex mappings. Therefore, a new class of nonconvex mapping i...

In this manuscript, we provide a generalization of the Cauchy integral to appropriate families of real-valued functions defined in R n. The results are motivated by a generalization of regulated functions. The founda-tional theory for this extended Cauchy integral is developed in detail in this self-contained work. We derive some properties for app...

for possible open access publication under the terms and conditions of the Creative Commons Attri-bution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Abstract: We investigate a class of one-dimensional (1D) Hamiltonian N-particle lattices whose 1 binary interactions are quadratic and/or quartic in the potential. We also include...

BACKGROUND. We provide a compartmental model for the transmission of some contagious illnesses in a population. The model is based on partial differential equations, and takes into account seven sub-populations which are, concretely, susceptible, exposed, infected (asymptomatic or symptomatic), quarantined, recovered and vaccinated individuals alon...

In this work, we propose a mathematical model that describes liver evolution and concentrations of alanine aminotransferase and aspartate aminotransferase in a group of rats damaged with carbon tetrachloride. Carbon tetrachloride was employed to induce cirrhosis. A second groups damaged with carbon tetrachloride was exposed simultaneously a plant e...

The integration of internationally sustainable practices into supply chain management methodologies is known as "green supply chain management". Reducing the supply chain's overall environmental impact is the main objective in order to improve corporate connections and the social, ecological, and economic ties with other nations. To accomplish appr...

The differential quadrature method is a well-known numerical approach for solving ordinary and partial differential equations. This work introduces an explicit form for the approximate solution using differential quadrature rules. Analogies with Taylor's expansion are presented. Some properties are formally discussed. An interpretation of the appro...

This paper proposes a novel fuzzy fractional extension of the Hermite-Hadamard, Hermite-Hadamard-Fejér, and Pachpatte type inequalities for up and down pre-invex fuzzy-number valued mappings. Using fuzzy fractional operators, we develop several generalizations, where well-known results fit as particular cases. Additionally, some non-trivial example...

The Boiti–Leon–Mana–Pempinelli Equation (BLMPE) is an essential mathematical model describing wave propagation in incompressible fluid dynamics. In the present manuscript, a novel generalization of the BLMPE is introduced, called herein the functional BLMPE (F-BLMPE), which involves different functions, including exponential, logarithmic and monoma...

Paradigms of nonlinear science may suggest that it is “the study of every single phenomenon” due to its interdisciplinary nature, which is a challenge requiring to be addressed by generating a systematic mathematical framework where the complexity of natural phenomena hints the requirement of identifying their commonalties and classifying their var...

Modern imaging strategies are paramount to studying living systems such as cells, bacteria, and fungi and their response to pathogens, toxicants, and nanomaterials as modulated by exposure and environmental factors. The need to understand the processes and mechanisms of damage, healing and cell survivability of living systems continues to motivate...

In this work, we present a system composed of three identical Duffing oscillators coupled bidirectionally. Starting from a Lagrangian that describes the system, an integral of motion is obtained by means of Noether’s theorem. The dynamics of the model is studied using bifurcation diagrams, Lyapunov exponents, time-series analysis, phase spaces, Poi...

In this manuscript, we characterize the kernel of the parabolic Dirac operator in an explicit way. More precisely, we will show that the members of this kernel equivalently satisfy a generalized div-curl system. Furthermore, it will be established that it is sufficient to know $4$ scalar solutions of the heat equation to construct explicitly a $C\e...

We investigate the dynamics of a SIRS epidemiological model taking into account cross-superdiffusion and delays in transmission, Beddington-DeAngelis incidence rate and Holling type-II treatment. The superdiffusion is induced by inter-country and inter-urban exchange. The linear stability analysis for the steady-state solutions is performed, and th...

In this work, we investigate the system formed by the equations div w ⃗ = g⃗ in bounded star-shaped domains of R . A Helmholtz-type decompo curl w sition theorem is established based on a general solution of the above-mentioned div-curl system. When g0 ≡ 0, we obtain a bounded right inverse of curl which is a divergence-free invariant. The restrict...

In the present work, decision trees are employed to determine the activation patterns in electromyographic signals in multiple muscles of interest. Due to the interaction of several muscles when performing a movement , it is common for several muscles to activate simultaneously. The problem is to determine if any muscle of interest is active and, i...

We consider a model for a cross-stitch lattice with onsite nonlinearity. The linear analysis and the determination of the homoclinic threshold for this model are carried out theoretically. In the case of a self-focusing nonlinearity, we show that the traveling bandgap soliton is possible as a result from the periodic excitation of the edge of the c...

In this article, families of solitary waves solutions of a general third-order nonlinear non-ohmic cable equation in cardio-electro-physiology are obtained using the $\exp(-\varphi(\xi))$-expansion method. In this equation, the unknown function represents the transmembrane current, and the exact soliton-like solutions are thoroughly derived using t...

In this work, we investigate the system formed by the equations $\text{div } \vec w=g_0$ and $\text{curl } \vec w=\vec g$ in bounded star-shaped domains of $\mathbb{R}^3$. A Helmholtz-type decomposition theorem is established based on a general solution of the above-mentioned div-curl system which was previously derived in the literature. When $g_0...

We investigate a generalization of the equation curl w=g to an arbitrary number n of dimensions, which is based on the well-known Moisil-Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains of Rn using classical operators from Clifford analysis. In the physically significant case n=3, two expl...

In this work, we propose an implicit finite-difference scheme to approximate the solutions of a generalization of the well-known Klein-Gordon-Zakharov system. More precisely, the system considered in this work is an extension to the spatially fractional case of the classical Klein-Gordon-Zakharov model, considering two different orders of different...

In this work, we propose a mathematical model for the efficiency of a silicon solar cell. The model is rigorously derived from continuity and transport assumptions, along with the Poisson equations to describe the behavior of charge carriers in a semiconductor. The photovoltaic phenomenon was thoroughly studied to develop the model, and some parame...

This manuscript studies a double fractional extended p-dimensional coupled Gross–Pitaevskii-type system. This system consists of two parabolic partial differential equations with equal interaction constants, coupling terms and spatial derivatives of the Riesz type. Associated with the mathematical model, there are energy and non-negative mass funct...

Background and objective. We present and analyze a nonstandard numerical method to solve an epidemic model with memory that describes the propagation of Ebola-type diseases. The epidemiological system contemplates the presence of sub-populations of susceptible, exposed, infected and recovered individuals, along with nonlinear interactions between t...

This present manuscript studies a nonlinear hyperbolic model in fractional form which generalizes the nonlinear Klein-Gordon system. The equation under investigation includes the presence of a time-fractional operator of the Caputo type. A space-fractional form of that equation with integer-order temporal derivative has been previously investigated...

Background and objective: In this work, we analyze the {\color{blue}spatial-temporal} dynamics of a susceptible-infected-recovered (SIR) epidemic model with time delays. To better describe the dynamical behavior of the model, we take into account the cumulative effects of diffusion in the population dynamics, and the time delays in both the Holling...

The present work is the first manuscript of the literature in which a numerical model that preserves the dissipation of free energy is proposed to solve a time-space fractional generalized nonlinear parabolic system. More precisely, we investigate an extension of the multidimensional heat equation with nonlinear reaction and fractional derivatives...