# G. Fernandez-AnayaUniversidad Iberoamericana Ciudad de México · Department of Physics and Mathematics

G. Fernandez-Anaya

Professor

Applied mathematics in multiple fields (Engineering, Physics, Finance, others)

## About

254

Publications

38,884

Reads

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1,710

Citations

Citations since 2017

Introduction

Additional affiliations

May 1987 - November 2021

January 1987 - October 2015

## Publications

Publications (254)

The Presnov decomposition for continuously differential vector fields consists of a gradient of a scalar field (dissipative term) and a vector field orthogonal to a radial vector of the origin (circulative or non-dissipative term). This paper uses the Presnov decomposition associated with a fractional-order Lorenz family to design algorithms that s...

This work studies the power-based formation control for a set of differential-drive mobile robots, as an extension of the traditional distance-based formation control schemes. The possible measurements of the Received Signal Strength Indicator (RSSI) coupled with the non-omnidirectional radiation pattern shape of their antennas are used as a feedba...

We are pleased to announce the launch of a special issue "Observability and Observer Design of Fractional-Order Nonlinear Systems". You are welcome to submit your article in an open access journal “Fractal and Fractional”.
Deadline for manuscript submissions: 30 September 2023
Please select the link below for more information. Thank you.
https:...

Sufficient and necessary conditions for a distributed‐order linear time invariant system to be positive real are derived in terms of linear matrix inequalities. The positive realness condition is derived for three of the most usual cases presented in literature, in the realm of distributed‐order linear time invariant systems. As an additional produ...

Fractional cosmology modifies the standard derivative to Caputo’s fractional derivative of order μ, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on μ and the age of the Universe tU. We estimate stringent constraints on μ using cosmic chronometers, Type Ia supernovae,...

Consensus or conflict agreements, and how these change over time, have significant consequences for understanding the network behavior of human beings, especially when it is necessary to have agreements to move companies and countries forward peacefully. This paper proposes a new Greatest Common Decision Maker (GCDM) aggregation voting procedure ap...

Consensus or conflict agreements, and how these change over time, have significant consequences for understanding the network behavior of human beings, especially when it is necessary to have agreements to move companies and countries forward peacefully. This paper proposes a new Greatest Common Decision Maker (GCDM) aggregation voting procedure ap...

Two new conformable spatial derivatives are defined and introduced to a classical viscous steady-state Navier–Stokes 1D model. The functions for the conformable derivatives have parameters [Formula: see text] and the fractional parameter [Formula: see text]. Analytical solutions for the velocity profile and flow rate are obtained from the conformab...

In the present work, some generalizations of the boundary crossing theorem and the zero exclusion principle are given for fractional order initialized systems. A new guardian map for the maximal stability interval is proposed as well as its relation with the boundary theorems is established. An extension of the technique for linear time invariant f...

Vector field decomposition is essential in physics and engineering in order to analyze several dynamical systems that appear in these areas. This paper proposes some novel stabilization methods, where the controller is based on the gradient of the smooth vector flow of a nonlinear fractional--order system. The gradient control is obtained from the...

This work presents an introductory observer theory for nonlinear dynamic systems modeled by the general conformable fractional derivative. General conformable exponential observers are defined, and Lyapunov-like stability methods are developed to design estimation algorithms. Two algorithms are presented to estimate unknown variables on conformable...

Fractional cosmology has emerged recently, based on the formalism of fractional calculus, which modifies the standard derivative to one fractional derivative of order $\alpha$. In this mathematical framework, the Friedmann equations are modified with an additional term, and the standard evolution of the cosmic species densities depends on the fract...

This paper presents a generalization of existing control methods. The proposal stands for a novel control structure that enforces the robust stabilization of a large class of physical and engineering systems, which are subject to the effect of nonlinearities, disturbances and uncertainties. The proposed scheme results as a state feedback plus a gen...

This paper presents the design of a novel methodology for robust stabilisation of distributed-order systems, which are subject to both matched and mismatched disturbances. Matched disturbances are coped through a nonlinear controller, while mismatched disturbances are rejected by pseudo-state feedback, whose gain is adjusted by solving a linear mat...

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...

Financial derivatives have grown in importance over the last 40 years with futures and options being actively traded on a daily basis throughout the world. The need to accurately price such financial instruments has, thus, also increased, which has given rise to several mathematical models among which is that of Black, Scholes, and Merton whose wid...

The objective of this work was to propose a Convective Conformable Mass Transfer model (CCMT) to estimate mass transfer
coe�cients (kLa) in bioreactors. The model employs a conformable derivative order operator (�), which is a function of the
electrode constant (kP), and this constant changes with the use of the electrode and the operating conditio...

Recently, a wide variety of non-integer, non-local and local linear operators have been developed, for example, fractional derivatives and conformal derivatives, establishing their properties, their links with non-linear equations and numerical methods for their solutions, giving rise to new mathematical models in practically all areas of science a...

The XXI Century has imposed the need to innovate and globalize all over around,
this demand better relationships of cooperation and collaboration among all kind of groups, organizations, countries, communities, and human beings. To understand inter-intra and network behaviors it is a priority in the process of decision making specially when worldwi...

Fractional calculus has been accomplished to model a wide range of phenomena. More recently, the conformable derivative has been receiving attention for its ability to reproduce some behaviors of the classical derivative. Zhao et al [3] presented an extension of the classical space derivative and the con formable fractional derivative, for a functi...

In classical calculus to obtain the n-th derivative of a product of functions, the Leibniz rule canbe used, however the problem is modified when composite functions are considered, for this type ofcase the formula of Faa di Bruno. There is a third case when compound functions receive a vectoras an argument. A proposed solution is described by Mishk...

Due to the substantial volatility faced by corporations, financial institutions, and even non-profit organizations, which is caused by both internal and external factors, among the latter are the constant globalization of transactions, asymmetric information, transaction costs, unforeseen variations in interest rates, and currently the impact of CO...

https://www.mdpi.com/journal/fractalfract/special_issues/GONIOM

This paper explores the concept of conformable derivative to produce a more general sliding motion, where the speed of convergence can be directly modulated during the design of the conformable operator. Through the analysis of a novel conformable derivative, a newer class of control systems can be proposed, which offer supplementary and entrancing...

Fractional sliding mode schemes possess the ability of compensating a large sort of continuous but not necessarily integer-order differentiable disturbances; however, the adjustment of the control parameters is usually difficult and is based on a heuristic process. Motivated by the approximation capabilities of fractional sliding modes, this articl...

Stability analysis plays an essential role in control systems design. This analysis can
be done using different techniques that show the equilibrium points are stable (or unstable). This paper focuses on fractional systems of order 0 <a < 1 modeled by the Atangana-Baleanu derivative of Riemann-Liouville type (ABR), which allows consistent modeling...

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...

Unmanned aerial vehicles (UAVs) have received much attention due to their capabilities to generate high-resolution aerial photographs that allow the creation of maps that can support the local governance of different communities. Aeronautical cartography is limited in rural communities due to different factors, such as bureaucratic, economic requir...

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...

New regulations allow peer-to-peer energy trading worldwide, empowering users while recognizing the prosumer as a critical stakeholder. In recent years, microgrids have surfaced as a distributed and embedded energy production alternative. This literature review analyses agent-based model systems with distinct approaches that model, control, and sup...

Distributed-order systems arise as a natural generalization of fractional- and integer-order systems, and these are commonly associated with slow and ultra-slow dynamics, which motivates designing robust schemes to enforce fast stabilization. This paper proposes a robust sliding mode controller that induces a
stable motion in a finite time, relying...

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...

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 work, a pair of observers are proposed for a class of nonlinear systems whose dynamics involve a generalized differential operator that encompasses the conformable derivatives. A generalized conformable exponential stability function, based on this derivative, is introduced in order to prove some Lyapunov-like theorems. These theorems help...

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 work presents a novel solution to Fractional-model equations, it is based on the applying of conformal derivative to fractional calculus and thus obtain a linear multi-term differential equations of integer order (Conformal-model). The main goal of this work is demonstrating the existences of the solutions for the Conformal-model, it is throug...

This paper studies a formation control scheme to achieve a ‘dispersion’ of a group of robots using the
Received Signal Strength Indication (RSSI) measurements of their on-board wireless nodes as feedback signals and their antenna radiation patterns (which is not omnidirectional in most of the cases)
as a distance sensor between pairs of robots. In...

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...

This article proposes two conformal Solow models (with and without migration), 1 accompanied by simulations for six Organisation for Economic Cooperation and Development 2 economies. The models are proposed by employing suitable Inada conditions on the Cobb-Douglas 3 function and making use of the truncated M-derivative for the Mittag-Leffler funct...

This article proposes two conformal Solow models (with and without migration), accompanied by simulations for six Organisation for Economic Co-operation and Development economies. The models are proposed by employing suitable Inada conditions on the Cobb–Douglas function and making use of the truncated M-derivative for the Mittag–Leffler function....

This paper proposes the study of a newer class of integro-differential operators, which allow analysing a more general family of dynamical systems, with not necessarily integer-order differentiable solutions, and based on Volterra integral equations of the second kind. One of the main advantages of the present study is that the proposed operators i...

Resumen Este trabajo aborda el problema de seguimiento de trayectorias de un robot móvil tipo diferencial considerando una extensión dinámica del modelo cinemático y, controlando un punto frontal situado a una cierta distancia perpendicular al eje medio de las rue-das. Se proponen dos tipos de controladores, un controlador PID de orden fraccionario...

This paper presents a novel model framework for complex urban traffic systems based on the interconnection of a dynamical multi-agent system in a macroscopic level. The agents describe all the types of street segments, intersections, sources and sinks of cars, modelling the behavior of the flow of vehicles through them as simple differential equati...

We developed a somewhat novel fractional-order calculus workbench as a certain generalization of Khalil's conformable derivative. Although every integer-order derivate can naturally be consistent with fully physical-sense problem's quotation, this is not the standard scenario of the non-integer-order derivatives, even aiming physics systems' modeli...

In this research, fractional dynamics has been incorporated into a nonlinear model of three coupled os- cillators to capture cardiac behavior more closely. We observe that in the case of the rhythms associated with a normal heart, the fractional orders are close to 1. For the spider-fearful individuals, fractional dy- namics were incorporated into...

Prediction of nonlinear and dynamic systems is a challenging task, however with the aid of machine learning techniques, particularly neural networks, is now possible to accomplish this objective. Most common neural networks used are the multilayer perceptron (MLP) and recurrent neural networks (RNN) using long-short term memory units (LSTM-RNN). In...

For Hilfer derivatives of the product of two functions, we present equations and inequalities, generalizing well‐known results for Caputo and Riemann‐Liouville derivatives. Using the Laplace transformation, we introduce a generalized distributed Mittag‐Leffler‐Hilfer stability and show two results for like‐Lyapunov stability. We also extend equatio...

From the definition of a generalized conformable spatial derivative, an exponential conformable function with three parameters $(a,b,\alpha)$ is proposed for a viscous and an inertial-viscous steady-state Navier-Stokes 1D models, obtaining analytical solutions for both generalized conformable models. The conformable models' parameters are optimized...

This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is ge...

In this work, we present a monoparametric family of piecewise linear systems to generate multiscroll attractors through a polynomial family defined by path curves that connect to the roots. The idea is to define path curves where the roots of a polynomial can take values by determining an initial and a final polynomial. As a consequence, structural...

Distributed-order calculus can be understood as a further generalisation of integer- and fractional-order calculus. Such a general case allows the modelling and understanding of a more extensive engineering and physical systems class. This paper proposes a controller design that enforces the predefined-time convergence of the solution of a distribu...

This paper focuses on the design of robust control laws for a heterogeneous multi-agent system composed of omnidirectional and differential-drive mobile robots under the leader–follower scheme and considering the distance and orientation measurements. It is assume that the agent leader is an omnidirectional mobile robot moving freely in the plane w...

We study stability of linear systems whose dynamics are described by systems of conformable fractional differential equations. We provide a framework in terms of behavioral system theory to develop a general modeling specification as well as stability conditions for conformable linear systems with a fractional differential order. We also provide su...

The aim of this work is to give a method to connect a set of polynomials having all of their roots inside the stability zone for fractional difference systems with the fractional discrete operator of Caputo. Due to the complexity of the stability zone, it is necessary to use its explicit description to build a polynomial family with zeros belonging...

Multicomponent-multiband fluxes of spim-charge carriers, whose components propagate mixed and synchronously, with \emph{a priori} nonzero incoming amplitudes, do not obey the standard unitarity condition on the scattering matrix for an arbitrary basis set. For such cases, we have derived a robust theoretical procedure, which is fundamental in quant...

En el presente trabajo de investigación, se desarrollan, se investigan, se analizan, se presentan y se estudian soluciones numéricas de modelos matemáticos de sistemas dinámicos de orden fraccionario que rigen el comportamiento de reactores de polimerización isotérmicos de dos tipos: primero, reactores poliméricos por lotes; segundo, reactores poli...

The relevant phase tunneling time limit of bandmixing-free holes, when the number of layer approaches to infinity, have been figured it out both analytically and numerically. We have demonstrated the existence of this elusive limit, by means of a breakthrough modelling of scattering quantities for multiband-multicomponent systems, \emph{via} a clos...

In this article two different controllers for the stabilization of a fractional-order discrete system in the left Caputo discrete delta
operator sense are given. The ﬁrst one acts by a fractional proportional pulse control, the second acts by a fractional feedback
control. These controllers are applied to fractional-order chaotic discrete dynamical...

In this paper, some estimators are proposed for nonlinear dynamical systems with the general conformable derivative. In order to analyze the stability of these estimators, some Lyapunov-like theorems are presented, taking into account finite-time stability. Thus, to prove these theorems, a stability function is defined based on the general conforma...

Chaotic dynamical systems are studied in this paper. In the models, integer order time derivatives are replaced with the Caputo fractional order counterparts. A Chebyshev spectral method is presented for the numerical approximation. In each of the systems considered, linear stability analysis is established. A range of chaotic behaviours are obtain...

We present a theoretical procedure, which is fundamental for unitarity preservation in multicomponent-multiband systems, for a synchronous mixed-particle quantum transport. This study focus the problem of (N×N) interacting components (with N≥2), in the framework of the envelope function approximation (EFA), and the standard unitary properties of th...

Conditions to establish Mittag-Leffler stability of solutions for nonlinear nonautonomous discrete Caputo-like fractional systems just from the linear associated system is shown. Mittag-Leffler stability for linear systems is tackled pointing out properties the matrix must satisfy. Additionally features on solutions for linear systems are included...

The purpose of this study is determining the region in the parameter space where the system is either stable or unstable. This work tackles two nonlinear models, one including the impact of the rate of temperature change on reactivity and another not including this term, with the goal to increase the understanding, identifying and associating the p...

This article shows a new focus of mathematic analysis for the Solow-Swan economic growth model, using the generalized conformal derivative Katugampola (KGCD). For this, under the same Solow-Swan model assumptions, the Inada conditions are extended, which, for the new model shown here, depending on the order of the KGCD. This order plays an importan...

This paper presents the extension of leader-follower behaviours, for the case of a combined set of kinematic models of omnidirectional and differential-drive wheeled mobile robots. The control strategies are based on the decentralized measurements of distance and heading angles. Combining the kinematic models, the control strategies produce the sta...