# J.F. Gómez-AguilarCONACyT-Tecnológico Nacional de México/CENIDET · Electronic

J.F. Gómez-Aguilar

PhD

## About

400

Publications

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9,779

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## Publications

Publications (400)

In this paper, the nonlinear refractive index cubic-quartic model is investigated using the couple of integration schemes namely, new extended generalized Kudryashov and improved tan(ϕ2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepac...

Nonlinear models of fractional order have elaborately been taken place in the research
field for their importance bearing the significant roles to depict the interior mechanisms
of complicated phenomena belonging to the nature. This present exploration deals with
the competent approach namely rational (G'/G)-expansion scheme to extract accurate...

This paper introduces some important dissipative problems that are recent and still of intermittent interest. The classical dynamics of Helmholtz and Kelvin–Helmholtz instability equations are modeled with the Riesz operator which incorporates the left- and right-sided of the Riemann–Liouville non-integer order operators to mimic naturally the phys...

A delay epidemic model is developed, with the susceptible population divided into three subclasses. In the main model, the well-known “Michaelis Menten Equation” is utilized to represent the effect of saturation. Infected, unaware, partially aware, and fully conscious compartments are included in the saturation incidence rates. The model includes a...

The diverse patterns of waves on the oceans yielded by the Kadomtsev Petviashvili-modified equal width (KP-mEW) equation are highlighted in this paper. Two recent established approaches such as the improved auxiliary equation technique and the enhanced rational (G′/G)-expansion scheme are utilized to construct wave solutions of the proposed governi...

This paper is devoted to exploring a new class of Atangana-Baleanu fractional stochastic differential systems driven by fractional Brownian motion with non-instantaneous impulsive effects. Using resolvent family, fixed point technique, and fractional calculus, we analysed the existence and uniqueness of the mild solution. Moreover, we discussed the...

In this paper, modified equal width Burgers’ equation has been investigated with the aid of unified method and bifurcation. This model has many applications in long wave transmission with dispersion and dissipation in nonlinear medium. The applied technique is efficient to retrieve exact solutions and their dynamic behaviors. The obtained solutions...

This article deals with constructing an operational matrix method based on fractional-order Lagrange polynomials to solve the non-local boundary value problems (BVPs) of fractional order arising in chemical reactor theory. In the proposed numerical technique, first, we determine the operational matrix of integer and fractional derivatives. Using th...

In this paper, the new iterative method with 휌-Laplace transform of getting the approximate solution of fractional diferential equations was proposed with Caputo generalized fractional derivative. The efect of the various value of order 훼 and
parameter 휌 in the solution of certain well known fractional diferential equation with Caputo generalized f...

In this paper, the new iterative method with ρ−Laplace transform of getting the approximate
solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of various value of order α and parameter ρ in the solution of certain well known
fractional differential equation with Caputo generalized fr...

In this paper, we consider two accurate iterative methods for solving fractional differential equations with power law and Mittag–Leffler kernel. We focused our attention on the stage-structured prey–predator model and several chaotic attractors of type Newton–Leipnik, Rabinovich–Fabrikant, Dadras, Aizawa, Thomas’ and 4 wings. The first algorithm i...

In this work, a methodology based on a neural network to solve fractal-fractional differential equations with a nonsingular and nonlocal kernel is proposed, the neural network is optimized by the Levenberg–Marquardt algorithm. For evaluating the neural network, different chaotic oscillators of variable order are solved and compared with algorithms...

The range of effectiveness of the novel corona virus, known as COVID-19, has been continuously spread worldwide with the severity of associated disease and effective variation in the rate of contact. This paper investigates the COVID-19 virus dynamics among the human population with the prediction of the size of epidemic and spreading time. Corona...

This manuscript examines the propagation of waves in a coaxial hollow infinite isotropic cylinder when exposed to a thermal heating source from the outer cylinder. For the mechanical conditions, the inner and outer cylinders are assumed to be displacement-free, in addition to a perfectly welded interface; while an insulation thermal condition is as...

The present manuscript investigates the action of the Hilfer fractional operator on the dynamics of resistor–capacitor (RC) and certain resistor–inductor-capacitor (RLC) electric circuits using the Laplace transform method alongside utilizing the negative binomial formula. The choice of Hilfer's operator here was basically based on its interpolatin...

This work shows the results of evaluating the corrosion type and rate (CR) in the 6061-T6 aluminum alloy exposed to ethanol-gasoline blends (E0, E10, E20, E30, E40, E60, E80, and E100) by analyzing electrochemical noise (EN) signals using the Shannon energy (SSE) and the synchrosqueezing transform (SST). The obtained results are compared against th...

The main purpose of this paper is to design a numerical method for solving the space–time-fractional advection-diffusion equation (STFADE). First, a finite difference scheme is applied to obtain the semi-discrete in time variable with convergence order $ \mathcal{O(\tau ^{2-\beta})}$. In the next, to discrete the spatial fractional derivati...

Using the first integral method (FIM) and the functional variable method (FVM), firstly we find the analytical solutions of conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE) and finally, we present numerical results in tables and charts.

Nonlinear evolution equations of non-integer order have elaborately been taken place in the research field for their importance bearing the significant role to delineate the interior characteristics of nonlinear wonders belonging to the nature. In this present effort, the time and space fractional nonlinear modified Camassa–Holm equation and the Sc...

This manuscript presents a bibliographic review on fractional-order control laws applied to robotics manipulators, robot vehicles, man-robot systems, as well as biologically inspired robots. The bibliographic review comprises a search about the control strategies design and definitions of fractional calculus used in several robot systems, as manipu...

This research proposes a novel transfer function based on the hyperbolic tangent and the Khalil conformable exponential function. The non-integer order transfer function offers a suitable neural network configuration because of its ability to adapt. Consequently, this function was introduced into neural network models for three experimental cases:...

The present research endeavor contains formulation of a new ψ‐Hilfer differential equation equipped with integral‐type subsidiary conditions. Utilizing Picard operator method, Banach contraction principle, and Gronwall inequality, we explore solution's properties of the underlying problem. We provide some assumptions to set up results related to un...

The sub-equation method is implemented to construct exact solutions for the conformable perturbed nonlinear Schrödinger equation. In this paper, we consider three different types of nonlinear perturbations: The quadratic–cubic law, the quadratic–quartic–quintic law, and the cubic–quintic–septic law. The properties of the conformable derivative are...

In this work, a class of chaotic nonlinear fractional systems of commensurate order called Liouvillian systems is considered to solve the problem of generalized synchronization. To solve this problem, the master and the slave systems are expressed in the Fractional Generalized Observability Canonical Form (FGOCF), then a fractional-order dynamical...

This research deals with a comparative numerical analysis of chaos in two systems with non-integer derivatives. The one-scroll system and circle equilibrium system with different hidden attractors are simulated considering the fractal derivative, Khalil and Atangana conformable derivatives, and the truncated M -derivative considering a constant and...

In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, suc...

In this paper a new definition of a local fractional derivative of order [Formula: see text] is introduced and applied to the study of the fractional nonlinear Schrödinger equation (FNLSE) with third-order dispersion and with Kerr and power laws of nonlinear refractive index. The analytical soliton solutions correspond to bright, dark and singular...

In this paper, a numerical method based on the Lagrangian piece-wise interpolation is proposed to solve variable-order fractal-fractional time delay equations with power law, exponential decay and Mittag-Leffler memories. These operators permit to describe physical phenomena with variable memory and fractal variable dimension. Numerical methods wer...

In this work, we studied the dynamics of a chaotic neural network using the fractional-conformable operator and non-integer order derivatives. We first systematically show the dynamics behavior of the network using the conformable operator. Then, we show the dynamics of the network using fractional-order derivatives. We compared the different effec...

This research deals with a comparative numerical analysis of chaos in two systems with non-integer derivatives. The one-scroll system and circle equilibrium system with different hidden attractors are simulated considering the fractal derivative, Khalil and Atangana conformable derivatives, and the truncated M-derivative considering a constant and...

This paper analyzes non-integer Hopfield neural network dynamics introducing the hyperbolic tangent transfer function generalized by the Mittag-Leffler function and the M-truncated derivative with constant and variable order. The novel neural network’s (ANN) behaviors are studied through their dynamics depicted in phase portraits and the 0-1 test t...

In this paper, we consider the equations of motion of a bar, of a given density, infinite in both direction, undergoing longitudinal vibrations under the action of an external load, and a stress-strain relationship using a fractional order differentiation operator with respect to the time variable. We use three types of fractional operators, two no...

The study of corrosion on aluminum alloys exposed to alternative fuels, such as ethanol, or bioethanol has been studied and presented in the literature by different researchers. Among signal processing methods reported in the literature can be found the statistical method (SM), the Fast Fourier Transform (FFT), and the Wavelet transform. In the pre...

Thermal convection suppresses the thermal stability and instability during the interaction between the magnetic fields because thermal convection is the most significant driver of time-dependent patterns of motion within magnetized and non-magnetized chaotic. In this manuscript, a mathematical modeling is proposed subject to the magnetohydrodynamic...

A new local fractional-order derivative operator is introduced and the Lakshmanan–Porsezian–Daniel (LPD) model is interpreted via this operator. New analytical solutions to the LPD equation is presented by Jacobi elliptic functions and an anzätz method. The complex-valued LPD equation includes a nonlinear term which is considered from three differe...

The aim of this paper is to provide a discussion of the amount of drug that should be administered to a patient by continuous intravenous infusion or oral dosing so that preventable adverse clinical events do not occur. To this end, we consider fractional- order, mammillary-type models that describe the dynamics of exchange of concentrations betwee...

The current study presents a new fractional-order three-echelon supply chain model. The chaotic behaviour of the proposed model is demonstrated, and after its synchronization is studied. To this end, a new control technique is offered for the proposed fractional-order system. In the design of the controller, it is assumed that all parameters of the...

Nonlinear fractional evolution equations are significant models for depicting intricate physical phenomena arise in nature. In this exploration, we concentrate to disentangle the space and time fractional nonlinear Schrodinger equation (NLSE), Korteweg-De Vries (KdV) equation and the Wazwaz-Benjamin-Bona-Mahony (WBBM) equation bearing the noteworth...

Due to increasing utilization of thermal treatment methods in medical science, the influence of blood’s perfusion has become totally dependent on the heat transfer analysis like heart and neurosurgery need temperature measurement during thermal treatment of the prostate. This manuscript presents the analytical treatment to the bioheat transfer Penn...

The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito (HSI) equation and the newly proposed extended (3+1)-dimensional Jimbo-Miwa (JM) equation with the help of a symbolic computation technique. By incorporating a direct variable transformation and utilizing Hirota’s bilinear form, multiple rogu...

The objective of this article is to consider a new class of fractional stochastic differential systems driven by the Rosenblatt process with impulses. We used fractional calculus, stochastic analysis, and Krasnoselskii's fixed point theorem to study the existence of piecewise continuous mild solutions for the proposed system. Further, we discussed...

Arbitrary order partial differential equations involving nonlinearity have mostly been utilized to portray interior behavior of numerous real-world phenomena during the couple of years. The research about the nonlinear optical context relating to saturable law, power law, triple-power law, dual-power law, logarithm law, polynomial low and mostly vi...

Fractional order nonlinear evolution equations have emerged in recent times as being very important model for depicting the interior behavior of nonlinear phenomena that exist in the real world. In particular, Schrodinger-type fractional nonlinear evolution equations constitute an aspect of the field of quantum mechanics. In this study, the (2+1)-d...

In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled with Adomian decomposition method has been defined and applied to solve the newly formulated nonlinear Schrödinger equation...

Following publication of the original article [1], the word ‘University’ was missed in the affiliation of the second author. The correct affiliation of the second author should be as follows: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21521, Saudi Arabia. The original paper has been updated.

This research considers an inverse source problem for fractional diffusion equation, containing fractional derivative with non-singular and non-local kernel, namely, Atangana-Baleanu fractional derivative. In our study, an explicit solution set is acquired via the expansion method and the overdetermination condition at a final time. The problem is...

In this work, we discussed the pathways and mechanisms responsible for transmission of nematode from bark beetles to pine trees and vice versa. The deterministic model, treated in this paper, seems quite robust in its qualitative behaviour. In order to check the fidelity of model and its implementation, we took the real data of pines which became i...

In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these operators is a locally uniformly convergent power series that can be chosen adequately to obtain a family of fractional operators and, in particular, the main existing fractional derivatives. Based on the conditions for the La...

In this article, a mathematical model for hypertensive or diabetic patients open to COVID-19 is considered along with a set of first-order nonlinear differential equations. Moreover, the method of piecewise arguments is used to discretize the continuous system. The mathematical system is said to reveal six equilibria, namely, extinction equilibrium...

In this paper, the generalized exponential rational function method is applied to obtain analytical solutions for the conformable (2+1)-dimensional chiral nonlinear Schrödinger equation. We obtain novel soliton, traveling waves and kink-type solutions with complex structures. We also present the two- and three-dimensional shapes for the real and im...

It is eminent that iterative learning control algorithm is of high significance due to its speciality of tracking control for systems developed from real-world phenomena that occurs repeatedly. Singular systems are well-known for their applications in network analysis, biological systems, economic systems, social systems, engineering systems, time-...

We present some space–time fractional differential equations (CEWE and CMEWE) solutions in this paper, which are useful in several fields. This type of equation describes the motion of waves and the way they travel in the media. So we deep into these equations to understand the properties of these waves through finding some solutions to these equat...

The present study implements the collective variable (CV) approach to examine an important Schrödinger equation known as the Fokas-Lenells equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters known as collective variables (CVs). This technique is straightforward and powerful for soliton solution extracti...

The objective of this manuscript is to study the collective variable (CV) technique to explore an important form of Schrödinger equation known as the Gerdjikov–Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters. These parameters are temporal position, amplitude, width, chirp, phase, and fre...

In this paper will use fractional calculus to analyze the model that describes a biofluid equipped with charged particles influenced by a magnetic field. For this purpose, the Atangana-Baleanu fractional operator in the Riemann-Liouville sense was used to solve the initial-boundary value problem. The fluid flow through a circular cylinder is influe...

In this paper, we propose a new numerical method based on two‐step Lagrange polynomial interpolation to get numerical simulations and adaptive anti‐synchronization schemes for two fractional conformable attractors of variable order. It was considered the fractional conformable derivative in Liouville‐Caputo sense. The novel numerical method was app...

A recently proposed numerical scheme for solving nonlinear ordinary differential equations with integer and non-integer Liouville-Caputo derivative is applied to three systems with chaotic solutions. The Adams-Bashforth scheme involving Lagrange interpolation and the fundamental theorem of fractional calculus. We provide the existence and uniquenes...

In the presented work, we present an accurate procedure, which is the spectral method, to find a solution to a certain class of the very important fractional (described by the Liouville–Caputo sense) models of the electrical RL, RC, and RLC circuits. This method is collocated using some important advantages of the generalized Legendre polynomials t...

s paper deals with the application of a novel variable-order and constant-order fractional derivative without singular kernel of Atangana-Koca type to describe the fractional
viscoelastic models, namely, fractional Maxwell model, fractional Kelvin-Voigt model, fractional Zener model and fractional Poynting-Thomson model. For each fractional viscoel...

Analytical solutions of the fractional wave equation via Caputo-Fabrizio fractional derivative are presented in this paper. For this analysis, three cases are considered, the classical, the damped and the damped with a source term defined by fractional wave equations. We show that these solutions are special cases of the time fractional equations w...

A nonlinear Schrödinger equation describing the polarization mode in an optical fiber which involves different physical terms such as quintic nonlinearity, self-steepening effect, and self-frequency shift is investigated in the present paper. The study goes on by adopting a field function and effective ansatzes to arrive at a highly nonlinear ODE w...

In this article, we study existence, uniqueness, and stability analysis in Hyer–Ulam settings of delay fractional differential equations with nonlinear singular p‐Laplacian operator ϕp. The fractional operators are taken in the Caputo sense. The fractional differential equation is converted into an integral form with the Green's theorem, also a fix...