Huitzilin Yépez Martínez - Academia.edu (original) (raw)
Papers by Huitzilin Yépez Martínez
AIMS Mathematics
In this study, the Nucci's reduction approach and the method of generalized projective Riccat... more In this study, the Nucci's reduction approach and the method of generalized projective Riccati equations (GPREs) were utilized to derive novel analytical solutions for the (1+1)-dimensional classical Boussinesq equations, the generalized reaction Duffing model, and the nonlinear Pochhammer-Chree equation. The nonlinear systems mentioned earlier have been solved using analytical methods, which impose certain limitations on the interaction parameters and the coefficients of the guess solutions. However, in the case of the double sub-equation guess solution, analytic solutions were allowed. The soliton solutions that were obtained through this method display real positive values for the wave phase transformation, which is a novel result in the application of the generalized projective Riccati method. In previous applications of this method, the real positive properties of the solutions were not thoroughly investigated.
International Journal of Modern Physics E, 2008
After reviewing some basic features of the temperature-governed phase-transitions in macroscopic ... more After reviewing some basic features of the temperature-governed phase-transitions in macroscopic systems and in atomic nuclei we consider non-thermal phase-transitions of nuclear structure in the example of cluster states. Phenomenological and semimicroscopical algebraic cluster models with identical interactions are applied to binary cluster systems of closed and non-closed shell clusters. Phase-transitions are observed in each case between the rotational (rigid molecule-like) and vibrational (shell-like) cluster states. The phase of this finite quantum system shows a quasi-dynamical symmetry.
We study the dispersion relation obtained from the semiclassical loop quantum gravity. This dispe... more We study the dispersion relation obtained from the semiclassical loop quantum gravity. This dispersion relation is considered for a photon system at finite temperatures and the changes to the Planck's radiation law, the Wien and Boltzmann laws are discussed. Corrections to the equation of state of the black body radiation are also obtained.
Journal of Physics: Conference Series, 2008
The possible role of the quasi-dynamical symmetry in nuclear clusterization is discussed. Two par... more The possible role of the quasi-dynamical symmetry in nuclear clusterization is discussed. Two particular examples are considered: i) the phases and phase-transitions of some algebraic cluster models, and ii) the clusterization in heavy nuclei. The interrelation of exotic (superdeformed, hyperdeformed) nuclear shapes and cluster-configurations are also investigated both for light, and for heavy nuclei, based on the dynamical and quasi-dynamical SU(3) symmetries, respectively.
Modern Physics Letters B, 2022
The sub-equation method is implemented to construct exact solutions for the conformable perturbed... more 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 discussed and applied with the help of a suitable wave transform that converts the governing model to a nonlinear ordinary differential equation. Furthermore, the order of the expected polynomial-type solution is obtained using the homogeneous balancing approach. Dark and singular soliton solutions are derived.
arXiv: Nuclear Theory, 2017
The Semimicroscopic Algebraic Cluster Model (SACM) is extended to heavy nuclei, making use of the... more The Semimicroscopic Algebraic Cluster Model (SACM) is extended to heavy nuclei, making use of the pseudo-SU(3) model. As a first step, the concept of forbiddenness will be resumed. One consequence of the forbiddenness is that the ground state of a nucleus can in general be described by two internally excited clusters. After that, the pseudo- SACM is formulated. The basis of pseudo-SACM is constructed, defin- ing each cluster within the united nucleus with the same oscillator fre- quency and deformation of the harmonic oscillator as a mean field and dividing the nucleons in those within the unique and normal orbitals, consistently for both clusters and the united nucleus. As test cases, this model is applied to 236U rightarrow\rightarrowrightarrow 210Pb+26Ne and 224Ra $\rightarrow} 210Pb+14C. Some spectroscopic factors will be calculated as predictions.
Indian Journal of Physics, 2019
By using improved F-expansion method (IFEM), we study density-dependent space-time-fractional dif... more By using improved F-expansion method (IFEM), we study density-dependent space-time-fractional diffusionreaction equation with quadratic nonlinearity (DDFDRE), which arises in mathematical biology. The fractional derivative is described in the sense of the CF derivative. Exact traveling wave solutions for DDFDRE are derived and expressed in terms of hyperbolic functions and rational functions. The IFEM is brief, efficient and easy to apply. It also can be used to solve many other fractional nonlinear evolution equations.
Journal of Interdisciplinary Mathematics, 2019
In this paper, with the aid of the Maple software, the new extended direct algebraic method is us... more In this paper, with the aid of the Maple software, the new extended direct algebraic method is used as a powerful method to constructs some new solutions to the well-known nonlinear models, namely, the simplified modified Camassa-Holm equation. The space-time fractional derivatives are defined in the sense of the new conformable fractional derivative. It is shown that the method is straightforward and effective mathematical tool for solving nonlinear evolution equations in mathematical physics and engineering.
Chinese Journal of Physics, 2019
Abstract The dynamics of solitons in birefringent optical fibers with weak nonlocal nonlinearity ... more Abstract The dynamics of solitons in birefringent optical fibers with weak nonlocal nonlinearity is studied in this paper, in presence of four-wave mixing terms in the governing model. There are three main types of exact one-soliton solutions retrieved for this dynamical system. The approach is based in the modified sub-equation extended method for the generalized hyperbolic and trigonometric functions for constructing new exact solutions of the governing coupled equations in birefringent optical fibers. Several constraint conditions naturally fall out during the course of integration of the corresponding coupled nonlinear partial differential equations.
Physical Review E, 2017
Different experimental studies have reported anomalous diffusion in brain tissues and notably thi... more Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark feature of these diseases. The diffusion in the axons can become to anomalous as a result from this abnormality. In this case the voltage propagation in axons is affected. Another hallmark feature of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increase, the voltage decreases. A similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
Advances in Difference Equations, 2016
In this work, we present an analysis based on a combination of the Laplace transform and homotopy... more In this work, we present an analysis based on a combination of the Laplace transform and homotopy methods in order to provide a new analytical approximated solutions of the fractional partial differential equations (FPDEs) in the Liouville-Caputo and Caputo-Fabrizio sense. So, a general scheme to find the approximated solutions of the FPDE is formulated. The effectiveness of this method is demonstrated by comparing exact solutions of the fractional equations proposed with the solutions here obtained.
Entropy, 2015
In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-F... more In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-Fabrizio derivatives are presented. The physical units of the system are preserved by introducing an auxiliary parameter σ. The input of the resulting equations is a constant and periodic source; for the Caputo case, we obtain the analytical solution, and the resulting equations are given in terms of the Mittag-Leffler function; for the Caputo-Fabrizio approach, the numerical solutions are obtained by the numerical Laplace transform algorithm. Our results show that the mechanical components exhibit viscoelastic behaviors producing temporal fractality at different scales and demonstrate the existence of Entropy 2015, 17 6290 material heterogeneities in the mechanical components. The Markovian nature of the model is recovered when the order of the fractional derivatives is equal to one.
Journal of Applied Mathematics, 2015
The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s f... more The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s first integral method are employed to obtain the exact solutions of the nonlinear space-time fractional ZKBBM equation and the nonlinear space-time fractional generalized Fisher equation. The power of this manageable method is presented by applying it to the above equations. Our approach provides first integrals in polynomial form with high accuracy. Exact analytical solutions are obtained through establishing first integrals. The present method is efficient and reliable, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics.
Physical Review C, 2003
A nuclear vibron model for nuclear molecules consisting of two clusters with inner structure is i... more A nuclear vibron model for nuclear molecules consisting of two clusters with inner structure is investigated. The Hamiltonian model has a U C 1 (6) U C 2 (6) U R (4)ʛSU C 1 (3) SU C 2 (3) SU R (3) dynamical symmetry. Applying a geometrical mapping, the relation of the parameter of the coherent state to the relative distance of the two clusters is deduced. The Hamiltonian model exhibits a minimum at relative distances different from zero. It is discussed how to deduce the potential, knowing the spectrum, and how to deduce the spectrum, knowing the potential. As a classical example the system 12 Cϩ 12 C is taken, where the spectrum is known and the internuclear potential can be obtained. This system serves as a consistency check of the method. Afterwards, the heavy system 96 Srϩ 146 Ba, playing a role as a subsystem of a possible three cluster molecule, is investigated and the possible structure of the spectrum is deduced. We show that in order to obtain a Hamiltonian consistent with a geometrical picture, the structure of this Hamiltonian is restricted. Ambiguities of the structure of the spectrum still exist but can be ordered into different classes.
In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-F... more In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-Fabrizio derivatives are presented. The physical units of the system are preserved by introducing an auxiliary parameter σ. The input of the resulting equations is a constant and periodic source; for the Caputo case, we obtain the analytical solution, and the resulting equations are given in terms of the Mittag-Leffler function; for the Caputo-Fabrizio approach, the numerical solutions are obtained by the numerical Laplace transform algorithm. Our results show that the mechanical components exhibit viscoelastic behaviors producing temporal fractality at different scales and demonstrate the existence of Entropy 2015, 17 6290 material heterogeneities in the mechanical components. The Markovian nature of the model is recovered when the order of the fractional derivatives is equal to one.
Una de las mas grandes dificultades con la que se enfrentan los estudiantes que por primera vez t... more Una de las mas grandes dificultades con la que se enfrentan los estudiantes que por primera vez tienen contacto con la fisica a nivel universitario, es la de plasmar en un problema sencillo, pero especifico, las ideas generales discutidas en clase. Esta dificultad para plantear y resolver problemas resulta ser un gran obstaculo para que los estudiantes avancen en el estudio de esta area del conocimiento. Esta obra presenta a los estudiantes universitarios del primer curso de fisica un conjunto de problemas y sus soluciones en el area de: la cinematica y dinamica de una particula, la cinematica y dinamica rotacional, los sistemas de particulas y las oscilaciones y ondas mecanicas; en los cuales se enfatizan las consideraciones fisicas necesarias para resolver los problemas. Esta obra debe verse por los estudiantes como un apoyo adicional a los libros de texto, como un libro que los acompana en el estudio de la mecanica y no como una fuente en donde pueden encontrar la solucion de las...
J. Comput. Appl. Math., 2019
In this paper, we present a new definition of fractional-order derivative with a smooth kernel ba... more In this paper, we present a new definition of fractional-order derivative with a smooth kernel based on the Caputo–Fabrizio fractional-order operator which takes into account some problems related with the conventional Caputo–Fabrizio factional-order derivative definition. The Modified-Caputo–Fabrizio fractional-order derivative here introduced presents some advantages when some approximated analytical methods are applied to solve non-linear fractional differential equations. We consider two approximated analytical methods to find analytical solutions for this novel operator; the homotopy analysis method (HAM) and the multi step homotopy analysis method (MHAM). The results obtained suggest that the introduction of the Modified-Caputo–Fabrizio fractional-order derivative can be applied in the future to many different scenarios in fractional dynamics.
Indian Journal of Physics
AIMS Mathematics
In this study, the Nucci's reduction approach and the method of generalized projective Riccat... more In this study, the Nucci's reduction approach and the method of generalized projective Riccati equations (GPREs) were utilized to derive novel analytical solutions for the (1+1)-dimensional classical Boussinesq equations, the generalized reaction Duffing model, and the nonlinear Pochhammer-Chree equation. The nonlinear systems mentioned earlier have been solved using analytical methods, which impose certain limitations on the interaction parameters and the coefficients of the guess solutions. However, in the case of the double sub-equation guess solution, analytic solutions were allowed. The soliton solutions that were obtained through this method display real positive values for the wave phase transformation, which is a novel result in the application of the generalized projective Riccati method. In previous applications of this method, the real positive properties of the solutions were not thoroughly investigated.
International Journal of Modern Physics E, 2008
After reviewing some basic features of the temperature-governed phase-transitions in macroscopic ... more After reviewing some basic features of the temperature-governed phase-transitions in macroscopic systems and in atomic nuclei we consider non-thermal phase-transitions of nuclear structure in the example of cluster states. Phenomenological and semimicroscopical algebraic cluster models with identical interactions are applied to binary cluster systems of closed and non-closed shell clusters. Phase-transitions are observed in each case between the rotational (rigid molecule-like) and vibrational (shell-like) cluster states. The phase of this finite quantum system shows a quasi-dynamical symmetry.
We study the dispersion relation obtained from the semiclassical loop quantum gravity. This dispe... more We study the dispersion relation obtained from the semiclassical loop quantum gravity. This dispersion relation is considered for a photon system at finite temperatures and the changes to the Planck's radiation law, the Wien and Boltzmann laws are discussed. Corrections to the equation of state of the black body radiation are also obtained.
Journal of Physics: Conference Series, 2008
The possible role of the quasi-dynamical symmetry in nuclear clusterization is discussed. Two par... more The possible role of the quasi-dynamical symmetry in nuclear clusterization is discussed. Two particular examples are considered: i) the phases and phase-transitions of some algebraic cluster models, and ii) the clusterization in heavy nuclei. The interrelation of exotic (superdeformed, hyperdeformed) nuclear shapes and cluster-configurations are also investigated both for light, and for heavy nuclei, based on the dynamical and quasi-dynamical SU(3) symmetries, respectively.
Modern Physics Letters B, 2022
The sub-equation method is implemented to construct exact solutions for the conformable perturbed... more 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 discussed and applied with the help of a suitable wave transform that converts the governing model to a nonlinear ordinary differential equation. Furthermore, the order of the expected polynomial-type solution is obtained using the homogeneous balancing approach. Dark and singular soliton solutions are derived.
arXiv: Nuclear Theory, 2017
The Semimicroscopic Algebraic Cluster Model (SACM) is extended to heavy nuclei, making use of the... more The Semimicroscopic Algebraic Cluster Model (SACM) is extended to heavy nuclei, making use of the pseudo-SU(3) model. As a first step, the concept of forbiddenness will be resumed. One consequence of the forbiddenness is that the ground state of a nucleus can in general be described by two internally excited clusters. After that, the pseudo- SACM is formulated. The basis of pseudo-SACM is constructed, defin- ing each cluster within the united nucleus with the same oscillator fre- quency and deformation of the harmonic oscillator as a mean field and dividing the nucleons in those within the unique and normal orbitals, consistently for both clusters and the united nucleus. As test cases, this model is applied to 236U rightarrow\rightarrowrightarrow 210Pb+26Ne and 224Ra $\rightarrow} 210Pb+14C. Some spectroscopic factors will be calculated as predictions.
Indian Journal of Physics, 2019
By using improved F-expansion method (IFEM), we study density-dependent space-time-fractional dif... more By using improved F-expansion method (IFEM), we study density-dependent space-time-fractional diffusionreaction equation with quadratic nonlinearity (DDFDRE), which arises in mathematical biology. The fractional derivative is described in the sense of the CF derivative. Exact traveling wave solutions for DDFDRE are derived and expressed in terms of hyperbolic functions and rational functions. The IFEM is brief, efficient and easy to apply. It also can be used to solve many other fractional nonlinear evolution equations.
Journal of Interdisciplinary Mathematics, 2019
In this paper, with the aid of the Maple software, the new extended direct algebraic method is us... more In this paper, with the aid of the Maple software, the new extended direct algebraic method is used as a powerful method to constructs some new solutions to the well-known nonlinear models, namely, the simplified modified Camassa-Holm equation. The space-time fractional derivatives are defined in the sense of the new conformable fractional derivative. It is shown that the method is straightforward and effective mathematical tool for solving nonlinear evolution equations in mathematical physics and engineering.
Chinese Journal of Physics, 2019
Abstract The dynamics of solitons in birefringent optical fibers with weak nonlocal nonlinearity ... more Abstract The dynamics of solitons in birefringent optical fibers with weak nonlocal nonlinearity is studied in this paper, in presence of four-wave mixing terms in the governing model. There are three main types of exact one-soliton solutions retrieved for this dynamical system. The approach is based in the modified sub-equation extended method for the generalized hyperbolic and trigonometric functions for constructing new exact solutions of the governing coupled equations in birefringent optical fibers. Several constraint conditions naturally fall out during the course of integration of the corresponding coupled nonlinear partial differential equations.
Physical Review E, 2017
Different experimental studies have reported anomalous diffusion in brain tissues and notably thi... more Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark feature of these diseases. The diffusion in the axons can become to anomalous as a result from this abnormality. In this case the voltage propagation in axons is affected. Another hallmark feature of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increase, the voltage decreases. A similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
Advances in Difference Equations, 2016
In this work, we present an analysis based on a combination of the Laplace transform and homotopy... more In this work, we present an analysis based on a combination of the Laplace transform and homotopy methods in order to provide a new analytical approximated solutions of the fractional partial differential equations (FPDEs) in the Liouville-Caputo and Caputo-Fabrizio sense. So, a general scheme to find the approximated solutions of the FPDE is formulated. The effectiveness of this method is demonstrated by comparing exact solutions of the fractional equations proposed with the solutions here obtained.
Entropy, 2015
In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-F... more In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-Fabrizio derivatives are presented. The physical units of the system are preserved by introducing an auxiliary parameter σ. The input of the resulting equations is a constant and periodic source; for the Caputo case, we obtain the analytical solution, and the resulting equations are given in terms of the Mittag-Leffler function; for the Caputo-Fabrizio approach, the numerical solutions are obtained by the numerical Laplace transform algorithm. Our results show that the mechanical components exhibit viscoelastic behaviors producing temporal fractality at different scales and demonstrate the existence of Entropy 2015, 17 6290 material heterogeneities in the mechanical components. The Markovian nature of the model is recovered when the order of the fractional derivatives is equal to one.
Journal of Applied Mathematics, 2015
The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s f... more The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s first integral method are employed to obtain the exact solutions of the nonlinear space-time fractional ZKBBM equation and the nonlinear space-time fractional generalized Fisher equation. The power of this manageable method is presented by applying it to the above equations. Our approach provides first integrals in polynomial form with high accuracy. Exact analytical solutions are obtained through establishing first integrals. The present method is efficient and reliable, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics.
Physical Review C, 2003
A nuclear vibron model for nuclear molecules consisting of two clusters with inner structure is i... more A nuclear vibron model for nuclear molecules consisting of two clusters with inner structure is investigated. The Hamiltonian model has a U C 1 (6) U C 2 (6) U R (4)ʛSU C 1 (3) SU C 2 (3) SU R (3) dynamical symmetry. Applying a geometrical mapping, the relation of the parameter of the coherent state to the relative distance of the two clusters is deduced. The Hamiltonian model exhibits a minimum at relative distances different from zero. It is discussed how to deduce the potential, knowing the spectrum, and how to deduce the spectrum, knowing the potential. As a classical example the system 12 Cϩ 12 C is taken, where the spectrum is known and the internuclear potential can be obtained. This system serves as a consistency check of the method. Afterwards, the heavy system 96 Srϩ 146 Ba, playing a role as a subsystem of a possible three cluster molecule, is investigated and the possible structure of the spectrum is deduced. We show that in order to obtain a Hamiltonian consistent with a geometrical picture, the structure of this Hamiltonian is restricted. Ambiguities of the structure of the spectrum still exist but can be ordered into different classes.
In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-F... more In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo-Fabrizio derivatives are presented. The physical units of the system are preserved by introducing an auxiliary parameter σ. The input of the resulting equations is a constant and periodic source; for the Caputo case, we obtain the analytical solution, and the resulting equations are given in terms of the Mittag-Leffler function; for the Caputo-Fabrizio approach, the numerical solutions are obtained by the numerical Laplace transform algorithm. Our results show that the mechanical components exhibit viscoelastic behaviors producing temporal fractality at different scales and demonstrate the existence of Entropy 2015, 17 6290 material heterogeneities in the mechanical components. The Markovian nature of the model is recovered when the order of the fractional derivatives is equal to one.
Una de las mas grandes dificultades con la que se enfrentan los estudiantes que por primera vez t... more Una de las mas grandes dificultades con la que se enfrentan los estudiantes que por primera vez tienen contacto con la fisica a nivel universitario, es la de plasmar en un problema sencillo, pero especifico, las ideas generales discutidas en clase. Esta dificultad para plantear y resolver problemas resulta ser un gran obstaculo para que los estudiantes avancen en el estudio de esta area del conocimiento. Esta obra presenta a los estudiantes universitarios del primer curso de fisica un conjunto de problemas y sus soluciones en el area de: la cinematica y dinamica de una particula, la cinematica y dinamica rotacional, los sistemas de particulas y las oscilaciones y ondas mecanicas; en los cuales se enfatizan las consideraciones fisicas necesarias para resolver los problemas. Esta obra debe verse por los estudiantes como un apoyo adicional a los libros de texto, como un libro que los acompana en el estudio de la mecanica y no como una fuente en donde pueden encontrar la solucion de las...
J. Comput. Appl. Math., 2019
In this paper, we present a new definition of fractional-order derivative with a smooth kernel ba... more In this paper, we present a new definition of fractional-order derivative with a smooth kernel based on the Caputo–Fabrizio fractional-order operator which takes into account some problems related with the conventional Caputo–Fabrizio factional-order derivative definition. The Modified-Caputo–Fabrizio fractional-order derivative here introduced presents some advantages when some approximated analytical methods are applied to solve non-linear fractional differential equations. We consider two approximated analytical methods to find analytical solutions for this novel operator; the homotopy analysis method (HAM) and the multi step homotopy analysis method (MHAM). The results obtained suggest that the introduction of the Modified-Caputo–Fabrizio fractional-order derivative can be applied in the future to many different scenarios in fractional dynamics.
Indian Journal of Physics