J.F. Gómez-Aguilar

• PhD
• Centro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp-IICBA)/UAEM

In this work, a mathematical model describing an infectious disease (pine wilt disease) caused by bark beetles has been studied. It has been analyzed qualitatively on the basis of “basic reproduction number” \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepac...

In this work, we obtain analytical solutions via Laplace transform of fractional electrical circuits by using the proportional Caputo derivative with power law. Numerical simulations were obtained to see the impact of the memory concept represented by the fractional parameter order. Also, we collect a lot of experimental data obtained in our labora...

This study presents a two dimensional mathematical model of heat transfer process, describing the melting process in a moving domain, which deals with the effect of temperature dependent heat generation and absorption. In many physical processes, as materials undergo phase change, they experience heat generation or heat loss as a result of various...

This study presents a fractional-order model to investigate the impact of human papillomavirus (HPV) on the progression of cervical cancer, aiming to provide a comprehensive mathematical framework. The classical integer-order model is restructured using the Atangana-Baleanu Caputo operator, which introduces fractional calculus into the disease dyna...

The current model describes the study of Darcy–Forchheimer 3D flow of MHD Maxwell hybrid nanofluid over a rotating disk with Arrhenius activation energy, heat generation, and variable thermal conductivity and mass diffusivity, taking into account with the effects of Marangoni phenomena. A hybrid nanofluid consisting of \(AA7072\) and \(AA7075\) alu...

Enclosure design cavities have a significant impact on thermal engineering methods and technologies, including electronics, power engines, thermal exchangers, heating systems, nuclear facilities and solar panels. This study aims to investigate the impact of MgO and Ag hybrid nanofluid inside a circular cavity under the influence of an inclined magn...

This work addresses the analytical solution of the fourth-Order Korteweg–de Vries (KdV4) equation, a nonlinear model describing the dynamics of optical soliton in (2+1) dimensions. To obtain exact results, we use the energy balance approach with two contemporary integration norms. The urgent need for precise mathematical representations in nonlinea...

This work proposes an optimized framework to enhance brightness while preserving textures and details in color digital images. The proposed method uses the conformable Gaussian and fractional Caputo–Fabrizio gradient to process the red (r), green (g), and blue (b) channels separately. The optimal models were reached via the Simulated Annealing algo...

The nonlinear space-time fractional Boussinesq and the space-time fractional (2+1)-dimensional breaking soliton equations are significant models for analyzing nonlinear dispersive waves, particularly the propagation of waves in shallow water, as well as acoustic, tidal, and tsunami waves. In this article, the new generalized (G′/G)\documentclass[12...

In this paper, we derive various new optical soliton solutions for the coupled Kuralay-IIA system of equations using an innovative solution approach known as the ϕ ⁶ − model expansion technique. This solution methodology employs a traveling wave transformation to reduce the considered problem into an easily solvable higher-order ordinary differenti...

This paper is concerned with the existence and functional stability of solutions to some class of integral-type implicit fractional-order differential equations using multi-strip subsidiary conditions. Contrary to the single-term fractional-order differential operators, in the present study, multi-term operators are involved, and the effect of the...

Due to their capacity to simulate intricate dynamic systems containing memory effects and non-local interactions, fractional differential equations have attracted a great deal of attention lately. This study examines multi-term fractional differential equations with variable type delay with the goal of illuminating their complex dynamics and analyt...

Fractional Partial Differential equations (FPDEs) are essential for modeling complex systems across various scientific and engineering areas. However, efficiently solving FPDEs presents significant computational challenges due to their inherent memory effects, often leading to increased execution times for numerical solutions. This study proposes a...

The purpose of this paper is to employ the fractional uncertain differential equation to model stock price and design an strategy to reduce the investment risk based on the optimization model. First, the two-factor fractional Liu uncertain model with the renewal process is presented. Then two algorithms are proposed to identify and separate the jum...

This paper centers around a space-fractional mathematical model for a fluvio-deltaic sedimentation process which involves a space-fractional derivative (Caputo derivative) and time dependent variable sediment flux to investigates the movement of shoreline in a sedimentary ocean basin. This model is a specific case of a basic shoreline model and ana...

The aim of the present work is to discuss the fractional mass-spring system with damping and driving force, considering a simple modification to the fractional derivatives with a non-singular kernel of the Atangana–Baleanu and Caputo–Fabrizio types. We introduce two novel modified fractional derivatives that offer advantages when the fractional dif...

This paper comprehensively considers the two-dimensional spatiotemporal dynamics of the Gierer-Meinhardt model, with the cross-diffusion coefficients as bifurcation parameters. Through multiscale analysis, the amplitude equation at the Turing threshold is derived. The paper sequentially analyzes the effects of cross-diffusion coefficients, Proporti...

In this article, we initially provided the relationship between the RL fractional integral and the Caputo fractional derivative of different orders. Additionally, it is clear from the literature that studies into boundary value problems involving multi‐term operators have been conducted recently, and the aforementioned idea is used in the formulati...

In this article, we study and analyze the two-dimensional time-fractional Cattaneo model with Riesz space distributed-order. To obtain approximate solutions of this type of fractional model the combined and effective numerical approach based on the ADI Galerkin method and the Legendre spectral method used the ADI Galerkin numerical method uses the...

Tumours have a complicated and dynamic system for care and rehabilitation and it is advisable to internalise possible techniques of approaches to address tumour ambiguity since it aids in the creation of plausible remedies. In recent years, fuzzy mathematical modelling has been extensively used as a beneficial tool for developing a profound and...

Infection with the hepatitis B virus (HBV) is a global health problem and may be controlled via appropriate treatment. We use fractional models to understand infectious diseases because fractional models help us understand treatments' effects on hepatitis B better than integer‐order models. In this article, we introduce a new mathematical model for...

Kinetic chemical reactions find applications across various fields. In industrial processes, they drive the production of essential materials like fertilizers and pharmaceuticals. In environmental science, they are crucial to understanding pollution dynamics. Additionally, in biochemistry, they underpin vital cellular processes, offering insights i...

The widespread use of computer hardware and software in society has led to the emergence of a type of criminal conduct known as cybercrime, which has become a major worldwide concern in the 21st century spanning multiple domains. As a result, in the present setting, academics and practitioners are showing a great deal of interest in conducting rese...

This study investigates the Stephan blowing impact on chemical reactive flow of THNF (trihybrid nanofluid) across a Riga plate with Marangoni convection and bio convection. The Riga plate consists of an electrode and magnet configuration on a plate. Around the vertical direction, the Lorentz force increases exponentially due to the fluid's electric...

Recently, some researchers have revisited the analysis of chlorine transportation in cylindrical pipes by deploying a coupling between the Laplace transform method and the complex analysis’ residue approach for inverting complex integrals. This method yielded interesting results after the incorporation of root-finding numerical schemes. Thus, away...

Multi-term time-fractional advection diffusion equations are vital for simulating a wide range of physical phenomena, including fluid dynamics and environmental transport processes. However, due to their natural complexity, these equations pose challenges for conventional numerical approaches. In this article, we develop a high order accurate metho...

This study uses fixed point theory and the Banach contraction principle to prove the existence, uniqueness, and stability of solutions to boundary value problems involving a Ψ-Caputo-type fractional differential equation. The conclusions are supported by illustrative cases, which raise the theoretical framework’s legitimacy. Fractional calculus is...

Recent SARS-CoV-2 XBB and BQ subvariants exhibit noticeably enhanced resistance to neutralizing antibodies, including in those persons who are vaccinated and have had breakthrough Omicron infection or who have received the bivalent mRNA booster. Nonlinear dynamics is an intriguing technique for explaining the dynamical behaviors of COVID-19 illness...

In this paper, a newfangled technique for edge detection that combines the Khalil conformable derivative and the Hessian matrix is developed and experimentally validated. The following main aspects are considered: (i) to attenuate image noise a Gaussian kernel inspired by the Khalil conformable derivative was developed. (ii) The spatial derivatives...

This study makes consideration of the recently devised Lax-integrable three-dimensional sixth-order Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation owing to the great relevance of higher-dimensional nonlinear evolution equation models in guiding various nonlinear phenomena in scientific domains. Thus, as only a little is known about the new mo...

This paper proposes a methodology for the diagnosis of electrical system conditions using fractional-order integral transforms for feature extraction. This work proposes three feature extraction algorithms using the Fractional Fourier Transform (FRFT), the Fourier Transform combined with the Mittag-Leffler function, and the Wavelet Transform (WT)....

Fractional-order models have been used in the study of COVID-19 to incorporate memory and hereditary properties into the systems. These models have been applied to analyze the dynamics and behavior of the novel coronavirus. Various fractional-order models have been proposed, including the SIR and SEIR models, with the addition of compartments such...

This paper seeks to present an optimization method to estimate the solutions of nonlinear oscillation equations of fractional order. The mentioned method is based on Bernstein polynomials (Bps). In the presented numerical approach, the operational matrices of the ordinary and fractional derivatives of Bernstein polynomials are utilized to estimate...

In this paper, a nonlinear generalized system of variable order (VO) of fractional differential equations (FDEs) based on the RDβi(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begi...

In this work, a Liouville–Caputo fractional order (FO) derivative for the mathematical system based on the accelerating universe in the modified gravity (AUMG), i.e. FO-AUMG is proposed to get more accurate solutions. The nonlinear dynamics of the FO-AUMG is classified into five dynamics. The performances of the designed nonlinear FO-AUMG are numer...

In this paper, we presented and proved a general Lyapunov's inequality for a class of fractional boundary problems (FBPs) involving a new fractional derivative, named $ \lambda $-Hilfer. We proved a criterion of existence which extended that of Lyapunov concerning the ordinary case. We used this criterion to solve the fractional differential equati...

Due to the lack of abundant literature with regard to the exact analytical solutions for the new higher-order Boussinesq-Burgers equations (HOBBE); of course, with the exception of a few that deployed the Hirota bilinear and ansatz methods, respectively, the present study is thus compelled to unravel more on the admissibility of additional exact so...

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...

This paper presents a controller-based synchronization scheme in a leader-follower architecture for chaotic maps of fractional variable-order. The proposed scheme demonstrates successful synchronization of three different chaotic maps through simulation results. The implementation on Arduino UNO boards is used to showcase the relatively low algorit...

MERS-CoV (Middle East Respiratory Syndrome Coronavirus) is a severe respiratory illness that poses a significant threat to the Arabic community and has the potential for global spread. In this paper, we present deterministic and stochastic models to study the dynamics of MERS infection within hosts. For the purpose of describing the dynamics of MER...

This study investigates the comprehensive optical soliton solutions to the (2+1)-dimensional nonlinear time-fractional Zoomeron equation and the space-time fractional nonlinear Chen-Lee-Liu equation using the extended Kudryashov technique. The newly defined beta derivative is used to conduct the fractional terms and investigate wide-spectral solito...

A mathematical model of discrete fractional equations with initial condition is constructed to study the tumor-immune interactions in this research. The model is a system of two nonlinear difference equations in the senseof Caputo fractional operator. The applications of Banach’s and Leray–Schauder’s fixed point theorems are usedto analyze the exis...

The outlet temperature and the thermal efficiency predictions of the PTSC are essential parameters in the solar thermal power system. Therefore, it is crucial to have a prediction model that can predict its spatiotemporal behavior to the greatest extent possible. For that, the present study provides improved models of the classical ANN model by usi...

In recent years, researchers have investigated boundary value problems of single terms and, in rare circumstances, multi-term fractional differential equations. Nonetheless, differential equations containing more than one fractional differential operator of the implicate type must be formulated in some cases. Therefore, bearing in mind the signific...

Many real-life problem is mathematically modeled by differential equations, there are always intrinsic phenomena that are not taken into account and can affect the behavior of such a model. For example, external forces can abruptly change the model. Sometimes these changes begin impulsively at some points and remain active over certain time interva...

In this research, a fractional-order technique for corner detection and image matching based on the Harris-Stephens algorithm and the Caputo-Fabrizio and Atangana-Baleanu derivatives is proposed and experimentally tested. It focuses on three main ideas: 1) To suppress image noise more effectively while maintaining better image fidelity, a fractiona...

This paper proposes an efficient procedure to estimate the fractional Black–Scholes model in time-dependent on the market prices of European options using the composition of the orthogonal Gegenbauer polynomials (GB polynomials) and the approximation of the fractional derivative dependent on the Caputo derivative. First, the payoff function’s singu...

This work aims to study the dynamics of a monkeypox infection model within the framework of fractal–fractional derivatives with power-type kernel. We discuss existence of unique solution to the model via fixed point arguments. The stability analysis of the system is verified in the sense of Ulam–Hyers (UH), generalized Ulam–Hyers (GUH), Ulam–Hyers–...

In this study, we give the notion of a piecewise modified Atangana-Baleanu-Caputo (mABC) fractional derivative and apply it to a tuberculosis model. This novel operator is a combination of classical derivative and the recently developed modified Atangana-Baleanu operator in the Caputo's sense. For this combination, we have considered the splitting...

In this paper, a general system of quadratically perturbed system of modified fractional differential equations (FDEs) is considered for the solution existence, solution uniqueness, stability results, numerical scheme and computational applications. The presumed perturbed system is more general and several preexisting problems become its special ca...

A chaotic analysis of thermal convection for non-Newtonian fluid is investigated by employing fractal–fractional differential operators. The most attractive novelty of this investigation is to retrieve the chaotic behavior of non-Newtonian fluid saturated by porosity for the chaotic behavior of Newtonian fluid saturated by porosity. The mathematica...

Distinct models involving nonlinearity are mostly appreciated for illustrating intricate phenomena arise in the nature. The new (3+1)-dimensional generalized nonlinear Boiti-Leon-Manna-Pempinelli (BLMP) model describes the dynamical behaviors of nonlinear waves arise in incompressible fluid. This present effort deals with the well-known governing B...

Classical Burgers’ equation is an indispensable dynamical evolution equation that is autonomously devised by Burgers and Harry Bateman in 1915 and 1948, respectively. This important model is featured through a nonlinear partial differential equation (NPDE). Furthermore, the model plays a crucial role in many areas of mathematical physics, including,...

The purpose of this work is to provide a stochastic framework based on the scale conjugate gradient neural networks (SCJGNNs) for solving the malaria disease model of pesticides and medication (MDMPM). The host and vector populations are divided in the mathematical form of the malaria through the pesticides and medication. The stochastic SCJGNNs pr...

Fractional order models involving nonlinearity are remarkable for having substantial application in real-world. The present determination is due to obtain applicable wave solutions of fractional order stochastic Bogoyavlenskii equation (SBE) in the viewpoint of stratonovich regarding multiplicative noise. Enhanced rational -expansion and improved...

Drug addiction is a neurological disorder, and it can be studied using mathematical modeling and computer simulations. The usage of methamphetamine is on the rise globally and has reached an epidemic level. Researchers have focused a lot of attention on the epidemic’s social repercussions. A model describing the dynamics of methamphetamine is intro...

The primary varicella-zoster virus (VZV) infection that causes chickenpox (also known as varicella), spreads quickly among people and, in severe circumstances, can cause to fever and encephalitis. In this paper, the Mittag-Leffler fractional operator is used to examine the mathematical representation of the VZV. Five fractional-order differential e...

This paper introduces the fractional-order Lagrange polynomials approach to solve initial value problems for pantograph delay and Riccati differential equations involving fractional-order derivatives. The fractional derivative is determined as per the idea of Caputo. First, operational matrices of fractional integration with fractional-order Lagran...

This paper proposes a new fuzzy mathematical programming method that was originally proposed to solve problems that can be formulated as LP models using data envelopment analysis (DEA) models and Karush–Kuhn–Tucker (KKT) conditions to evaluate the efficiency of fuzzy systems. KKT condition (also learned as the Kuhn-Tucker condition) is a first deri...

The present manuscript gives an overview of how two-dimensional heat diffusion models underwent a fractional transformation, system coupling as well as solution treatment. The governing diffusion models, which are endowed with Caputo's fractional-order derivatives in time $ t $, are suitably coupled using the (1) convection phenomenon, (2) interfac...

The main goal of this work is to present a new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler non-singular kernel and strong memory. This proposal presents important advantages when specific initial conditions are impossed. The new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler...

The aim of this paper is to provide a mathematical study of the amount of drug administered as a continuous intravenous infusion or oral dose. For this purpose, we consider fractional-order mammillary-type models describing the anomalous dynamics of exchange of concentrations between compartments at, constant input rates, power-law type, and in the...

The authors present a method to solve differential equations with any kind of initial and boundary conditions using the Fibonacci neural network (FNN). Fibonacci polynomial has been used as an activation function in the middle layer to construct the FNN. The trial solution of the differential equation is considered as the output of the feed-forward...

Distinct models involving nonlinearity are mostly appreciated for illustrating intricate phenomena arise in the nature. The new (3 + 1)-dimensional generalized nonlinear Boiti-Leon-Manna-Pempinelli (BLMP) model describes the dynamical behaviors of nonlinear waves arise in incompressible fluid. This present effort deals with the well-known governing...

This paper considers stability analysis of a Susceptible-Exposed-Infected-Recovered-Virus (SEIRV) model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission. The Lyapunov function using Volterra–Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium...

The study of waves emerged in magnetic field bears worth mentioning roles for describing the nematic liquid crystal and the chiral soliton lattice. This exploration deals with the non-linear coupled Konno-Oono model relating to the magnetic field. The solitary wave solutions relating to the magnetic field have great importance for better understand...

This work deals with a numerical analysis of a Complex Lorenz system generalized by the truncated M-derivative (M-ℂLM). First, we carry out 10000 random simulations based on the Monte Carlo principle and the 0–1 test with the chaos decision tree to show that, on average, the M-ℂLM depicts chaotic dynamics because its growth rate is 0.9611±0.0183. N...

The current manuscript studies a discrete-time phytoplankton-zooplankton model with Holling type-II response. The original model is modified by considering the condition that the phytoplankton population is getting infected with an external toxic substance. To obtain the discrete counterpart from a continuous-time system, Euler's forward method is...

The performance of the hyperbolic-numerical inverse Laplace transform (hyperbolic-NILT) method is evaluated when it is used to solve time-fractional ordinary and partial differential equations. With this purpose, the formalistic fractionalization approach of Gompertz and diffusion equations are used as model problems, i.e., in the Gompertz and diff...

The purpose of the paper is to implement the collective variable method to investigate the generalized complex Ginzburg–Landau equation, which characterizes the kinetics of solitons in respect of pulse parameters for fiber optics. The statistical simulations of the interacting system of ordinary differential equations that reflect all the collectiv...

In this work, an internal combustion (IC) engine air-fuel ratio (AFR) control system is presented and evaluated by simulation. The control scheme aims to regulate the overall air-fuel ratio (AFRoverall) in an IC engine fueled with a hydrogen-enriched ethanol-gasoline blend (E10) as fast as possible. The control scheme designed and developed in this...

It becomes an interesting part for the researchers to analyze the dynamical behavior of soliton propagation in optical fibers for trans-oceanic and trans-continental distances. In this paper, we desire to retrieve distinct and innovative accurate wave solutions to the dual core optical fiber nonlinear equations by adopting the improved tanh method...

This paper discusses the analytical solution of fractional differential equations involving the Hilfer fractional derivative. The procedure adopted is the modified iterative Laplace transform method which uses simple calculation and has a higher convergence rate. The approach is such that for distinct values of the type of the Hilfer fractional der...

This paper is performed to extract solitons and other solitary wave solutions of the generalized third-order nonlinear Schrödinger model by implementing two compatible schemes like improved auxiliary equation and enhanced rational (G ' ∕G)-expansion methods. The mentioned equation governs extensive applications in numerous disciplines of engineerin...

The intension of the present study is to solve the nonlinear biological susceptible, infected and recovered (SIR) models using Feed-Forward Artificial Neural Networks (FFANN) optimized with global search of genetic algorithm aided with rapid local search interior-point IP algorithms, i.e., FEANN-GAIP. An error-based cost function is formulated by e...

We consider the equations of motion of a bar, with given density, infinite in both directions, subjected to longitudinal vibrations under the action of an external load, and a stress-strain relation represented by a fractional-order operator. Using three types of fractional operators, the initial-boundary value problems associated with the describe...