Juan NapolesNational University of the Northeast | UNNE · Department of Mathematics (Faculty of Natural and Exact Sciences and Surveying)
Juan Napoles
PhD in Mathematical Sciences
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299
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Introduction
En este momento, si bien no he abandonado completamente el estudio de los sistemas bidimensionales de orden entero, tenemos dos direcciones de trabajo perfectamente definidas:
1) El cálculo fraccionario local y sus aplicaciones.
2) El q calculus y las derivadas de tipo q uniforme.
Sobre todo relacionadas con la Teoría de la Estabilidad, en particular el Segundo Método de Lyapunov.
Additional affiliations
August 2008 - present
December 1999 - present
August 1998 - July 2008
Education
January 1992 - December 1994
September 1988 - July 1989
February 1986 - July 1986
Publications
Publications (299)
In this study, some inequalities of Hermite–Hadamard type for integrals arising in conformable fractional calculus are presented. Numerous known versions are recovered as special cases. We also illustrate our findings via applications to modified Bessel functions, special means, and midpoint approximations.
In the present study, several new generalized integralinequalities of the Hadamard and Simpson-type are obtained. Theresults were obtained for functions whose first and third derivativesare either convex or satisfy the Lipschitz condition or the conditionsof the Lagrange theorem. In a particular case, these results not onlyconfirm but also improve...
In this paper using generalized integral operators, we first obtain new interesting generalized improved Hölder integral inequality. Also, after deriving a new lemma using these operators, we give two results via quasi-convex functions. Some special cases of our results recapture known results. At the end, some error estimates are given to illustra...
En esta conferencia, presentamos algunos resultados sobre operadores
integrales y discutimos varias direcciones de trabajo.
Una de las nociones básicas en cualquier curso de Cálculo, es el de Derivada y su definición, en términos de un cierto cociente incremental, es una de las herramientas más poderosas en las aplicaciones. Sin esta noción, el estudio de multitud de aplicaciones, sería poco menos que imposible. Desde el 30 de Septiembre de 1695, cuando L'Hopital le pre...
PUIRJ (Partners Universal International Research Journal) is an international publisher of open access, peer-reviewed journals quarterly publishing full-length papers four times a year. The journal publishes original research articles from multiple disciplines.
The primary goal of the journal is to publish research articles for wide dissemination t...
In this Conference, we present some results on integral operators and we discussed various directions of work.
In this Conference we present new mathematical tools to model and solve problems in Engineering.
In this work, using the definitions of convex functions and h-convex functions, new
Hermite–Hadamard type inequalities are presented using the framework of q-calculus. We prove inequalities for the qa - and qb -definite integrals of functions which have a convex or general convex qa - or qb -derivative. These inequalities have consequences for q-in...
In this paper we introduce a Gaussian-like function, as a solution of a Conformable Differential Equation (CDE) of order 0<alpha<= 1, able to describe the nearest-neighbor energy-level spacing distribution of quantum systems; where alpha can be identified as the level-repulsion parameter. In addition, we study some properties of conformable operato...
It is very difficult to converge the trend of modern physical chemistry starting from Quantum
Chemistry to Surface Chemistry including the Computer applications on Chemistry.
Let us highlight one by one the Chapter Link:
➢ Quantum Chemistry & Statistical Thermodynamics.
➢ Computer & Statistical application of Physical Chemistry .
➢ Photo Physical C...
In this paper, we study the properties and various results of the generalized Laplace Equation, using a previously defined and studied generalized derivative. We discuss the solution of this mathematical problem with conditions of the Dirichlet type and Neumann type. The results obtained are illustrated using various examples, by modeling the solut...
In this conference, we take a tour of some integral inequalities, mainly the Hermite-Hadamard Inequality. We present the most current working directions and some open problems.
En esta Conferencia, presentamos algunos resultados sobre desigualdades integrales, en el marco de operadores integrales fraccionarios y generalizados, analizamos sus principales propiedades y las técnicas de trabajo más utilizadas.
4th International Conference on Pure and Applied Mathematics
(ICPAM-VAN 2022)
VAN, TURKEY
Dear Colleague,
Due to the global spread of COVID-19, we organize a virtual conference entitled 4th International Conference on Pure and Applied Mathematics (ICPAM-VAN 2022), which will be held on June 22-23, 2022. For more information, you can http://icpam.yy...
Today’s generation is relying not only on nutrition and satisfying their hunger but also find nutritional properties in their foods. For satisfying the demand of consumers’ overall health benefits, the concept of functional foods come into existence. Health benefits of probiotic drinks gives a new pace to traditional drinks. Probiotics are live str...
In this paper, we establish some new type integral inequalities for differentiable (h, m)-convex modified of the second type functions, using generalized integrals.
In this work, we obtain new inequalities of the Hermite-Hadamard type, using generalized fractional integrals. The results obtained contain, as particular cases, several of those reported in the literature.
In this paper, we establish new Hermite-Hadamard inequalities for h-convex functions, with in the framework of a previously defined generalized integral. The results obtained, generalize or complete, several reported in the literature. Some final remarks show the strength and scope of our results.
The concept of validity has been explored from diverse perspectives, where the argument-based approach provides a mediation between the qualitative and the quantitative. In the case of special education research, the problem of validity is accentuated in the face of frequently small samples and in relatively complex contexts. The present work addre...
This paper investigates existence, uniqueness, and Ulam’s stability results for a nonlinear implicit \phi-Hilfer FBVP describing Navier model with NIBCs. By Banach’s fixed point theorem, the unique property is established. Meanwhile, existence results are proved by using the fixed point theory of Leray-Schauder’s and Krasnoselskii’s types. In addit...
As timely renovation of artificial ideology about authenticity of nature in proportion to contemporaneous historical background of remarkable highlight of microcosmic configuration of matter, “Homogenous Cosmos Originated from Unique Genesis” is innovative cosmos redefinition and thoroughly coherent PNT dynamics about universal existence & motion a...
En esta propuesta, pretendemos mostrar cómo podemos utilizar datos e informaciones de la vida real, por ejemplo la pandemia del COVID19, para enriquecer nuestras prácticas pedagógicas.
Podemos enmarcar nuestra propuesta, en la Matemática Realista, una corriente que ha ido ganado su lugar en los últimos años.
In this work, we present some results related to obtaining and studying the solutions of generalized differential equations, by means of a certain generalized integral transformation.
Special issue of the journal VIDYA, open to researchers in Mathematics Education.
In this paper, we present some results for a fractional derivative of type q uniform defined by the authors in a previous work, and which are generalizations of known classical results of ordinary calculus.
In this paper, some new inequalities of the Hermite-Hadamard type are obtained for the classes of functions whose absolute values of the N-derivatives are (h, m)-convex. The results obtained in this work extend and improve some of those reported in the literature.
In this paper, we obtained new integral inequalities of the Hermite-Hadamard type for convex and quasi-convex functions in a generalized context.
The article introduces a new concept of convexity of a function: $(s,m_{1},m_{2})$-convex functions. This class of functions combines a number of convexity types found in the literature. Some properties of $(s,m_{1},m_{2})$-convexities are established and simple examples of functions belonging to this class are given. On the basis of the proved ide...
The article introduces a new concept of convexity of a function: $(s,m_{1},m_{2})$-convex functions. This class of functions combines a number of convexity types found in the literature. Some properties of $(s,m_{1},m_{2})$-convexities are established and simple examples of functions belonging to this class are given. On the basis of the proved ide...
In this article, using the concept proposed reciently by the author, of a Generalized k-Proportional Fractional Integral Operators with General Kernel, new integral inequalities are obtained for convex functions. It is shown that several known results are particular cases of the proposed inequalities and in the end new directions of work are provid...
In this paper we obtain some extensions of the Hermite-Hadamard Inequality for functions (h, m)-convex modified of second type, using the framework of weighted integrals. We show throughout the work that several known results are particular cases of ours.
En este trabajo, presentamos algunos resultados para una derivada generalizada multi-índice, recientemente definida por los autores (ver [8]), que están estrechamente relacionados a algunos del cálculo clásico y que contiene varios resultados conocidos del cálculo generalizado local. La resolución del Problema de Sturm-Liouville es también abor-dad...
Using the definition of functions (h;m)-convex modi´fied of second type, various refinements of the classic Hermite-Hadamard Inequality are obtained in the framework of weighted integrals. To illustrate the generality of the results obtained, several results reported in the literature are presented, which are particular cases of ours.
Resumen. Usando la definición de funciones (h,m)-convexa modificada de segundo tipo (recientemente definida), se obtienen varios refinamientos de la desigualdad clásica de Hermite-Hadamard, utilizando el marco de integrales pesadas. En el trabajo mostramos que varios de los resultados reportados de la literatura son casos particulares de los nuestr...
Fractional calculus has a very particular two-sided characteristic; on the one hand it is as old as ordinary (integer) calculus and on the other, in the last 40 years it has multiplied its applications in a wide range of areas and dissimilar themes. As a result, the number of researchers and publications is constantly increasing year a er year, fro...
Remarkable highlight of microcosmic configuration of matter, especially the factuality that discretionary particles in cosmos are mutually convertible is always in orientation towards complete induction day by day has made the homogenous profile of cosmos more and more explicit in our rational purview.
Whereas, is cosmos really homogenous originat...
In this work, using the definition of functions (h, m)-convex modified of second type, various refinements of the classic Hermite-Hadamard Inequality are presented using the framework of weighted integrals. Throughout the work, we show that various known results from the literature can be obtained as particular cases of ours.
In this lecturer, we review some of the results obtained in recent
years, which have set a trend in the development of this discipline.
In this paper, we study the boundedness and continuability of the solutions of a generalized Liénard type system, using fractional derivatives of the local type. We obtain sufficient conditions for the solutions to be bounded and continuous by a suitably defined Lyapunov function. We illustrate the results and suggest extensions to asymptotic stabi...
Integral inequalities via generalized fractional operators Resumen In this paper, we present some lines of work in the field of Integral Inequalities, linked with fractional and generalized integral operators.
In this work we define a generalized Laplace transform and establish some of its fundamental properties, in addition, we show that it contains as particular cases, several known from the literature, including the classical Laplace transform. In addition, its application to the resolution of generalized differential equations is shown.
En este trabajo, presentamos algunas ideas sobre la historia del concepto estabilidad según Lyapunov, sus desarrollos actuales y problemas abiertos. Palabras claves: Lyapunov, Teoría de la estabilidad, historia de las matemáticas Abstract In this work some ideas about the history of the stability concept from Lyapunov, its development until now and...
In this paper, by using the k-generalized fractional integrals, we establish certain integral inequalities for the Chebyshev functional in case of synchronous function. The obtained inequalities generalize several known integral inequalities.
Resumen En este trabajo, presentamos algunas ideas sobre la historia del concepto estabilidad según Lyapunov, sus desarrollos actuales y problemas abiertos. Palabras claves: Lyapunov, Teoría de la estabilidad, historia de las matemáticas Abstract In this work some ideas about the history of the stability concept from Lyapunov, its development until...
In the present paper, the main theorems of the classical Laplace transform are generalized in the non-conforming Laplace transform with nucleus e t −α. We calculate the Laplace transform of non-conforming agreement of this kernel from some elementary functions and establish the non-conforming version of the transform of the successive derivative, t...
In this communication, using a generalized conformable differential operator, a simulation
of the well-known Newton’s law of cooling is made. In particular, we use the conformable t^{1-\alpha}, e^(1-\alpha)t and non-conformable t^\alpha kernels. The analytical solution for each kernel is given in terms of the conformable order derivative 0 < \alpha...
El concepto de validez ha sido explorado desde perspectivas diversas, donde el enfoque basado en argumentos provee una mediación entre lo cualitativo y lo cuantitativo. En el caso de las investigaciones de la educación especial, el problema de la validez se acentúa frente a muestras frecuentemente pequeñas y en contextos relativamente complejos. El...
In this article, by utilizing the monotone iterative strategy coupled with the strategy of upper and lower solutions, we get the existence of extremal iteration solution to generalized differential equations under boundary conditions of type Riemann-Stieltjes, which at the same time provides the principle of comparison for these solutions. The resu...
In this paper, we present new inequalities of the Hermite-Hadamard type for generalized ϕ-convex functions, within the framework of non conformable fractional integrals.
In this work, a new generalized fractional integral is defined and studied, and different relationships (equalities and inequalities) are obtained, which have as particular cases several of those reported in the literature. Hermite-Hadamard type inequalities are obtained for different kinds of functions such as symmetric, convex symmetric, Wright-q...
In this Conference, we present a geometric interpretation of the Generalized Integrals, previ-
ously de�ned by the author, which contain as a particular case, the Riemann-Liouville fractional
integral.
Nos enfrentamos a uno de los mayores retos que ha sufrido la Humanidad, esto no solo se traduce en la propia existencia, suficientemente importante por si sola, si no en la supervivencia de un proceso social que incluye como uno de sus pilares la Educación, en particular la Educación Matemática. Creemos que debemos enfrentar hoy, el quehacer en las...
RESUMEN Uno de los programas de matemática dinámica más consultados y utilizados en la enseñanza y aprendizaje de la matemática es el programa GeoGebra, que mezcla la funcionalidad de un procesador geométrico y algebraico, muy fácil de usar y que resulta ser una poderosa herramienta, es un software que reúne geometría, álgebra, estadística y cálcul...
In this paper, we have established some generalized inequalities of Hermite–Hadamard–Fejér type for generalized integrals. The results obtained are applied for fractional integrals of various type and therefore contain some previous results reported in the literature.
In this paper we present some asymptotic properties of a generalized
differential equation, using a derivative notion general which contains as
particular cases many of the differential operators reported in the literature. In
particular, the stability in the Hyers-Ullam sense of a generalized differential
equation of order alpha is studied.
In this paper we present some criteria on the oscillation of solutions of
a Non Conformable Differential Equations of alpha +alpha order, under natural
considerations. The local derivative considered was defined by the author
in a previous work and a change of variables is used to transform the generalized
differential equation into an ordinary dif...
In this paper, we present some new integral inequalities, defined within the framework of
generalized integrals.
En este cursillo, presentamos dos de las desigualdades integrales más importantes y de mayor aplicación en el cálculo aproximado de integrales defi�nidas: las desigualdades de Hermite-Hadamard y de Hermite-Hadamard-Fejer, una de las pocas formas de acotar el
valor medio de una función, en este caso para diferentes nociones de convexidad.
UNIDAD I: VARIABLES. FUNCIONES.
Coordenadas cartesianas ortogonales y polares. Transformación (proyección).
Funciones. Campo de definición de una función. Cotas. Clasificación de las funciones.
Composición de funciones. Funciones monótonas. Funciones escalonadas.
En esta Conferencia, presentamos algunos operadores integrales fraccionarios y generalizados, y analizamos su relación con distintos operadores diferenciales locales y presentamos algunas direcciones de trabajo abiertas.
In this article, using the Riccati-type transformation, we study the oscillatory nature of the solutions of the generalized differential equation and give some criteria of the Kamenev type that generalizes several well-known results on the topic.
In this work, the well-known Minkowski inequality is studied, using a generalized fractional integral operator, defined and studied by authors in a previous work. Relationships with known results are established throughout the work and in conclusions.
In this paper, we study the oscillatory character of a generalized di-ferential equation of order alpha
with alpha in (0; 1]. Generalized criteria are obtained, of type Kamenev, which are extensions of several
known in the literature both integer and fractional.
In the present paper, the main theorems of the classical Laplace transform are generalized in the non-conforming Laplace transform with nucleus e t −α. We calculate the Laplace transform of non-conforming agreement of this kernel from some elementary functions and establish the non-conforming version of the transform of the successive derivative, t...
We introduce a definition of a generalized conformable derivative of order α > 0 (where this parameter does not need to be integer), with which we overcome some deficiencies of known local derivatives, conformable or not. This definition allows us to compute fractional derivatives of functions defined on any open set on the real line (and not just...
In this paper, we use new definition of left and right conformable fractional integral to obtain some new inequalities. The results obtained are refinements of existing results.
In this paper, we present two qualitative results concerning the solutions of nonlinear generalized differential equations, with a local derivative defined by the authors in previous works. The first result covers the boundedness of solutions while the second one discusses when all the solutions are in L$^{2}$.
In this article we present a second-order differential equation in the framework of the derivative N, and various qualitative properties of the solutions are studied, firstly conditions are obtained under which the equation under study has a non-continuity solution at infinity. Later we study the conditions for the prolongation of the solutions and...
In this paper, the author introduces the generalized fractional Hilfer integral and derivative of order µ, which are natural extensions of some recently defined fractional operators.
In this paper we present an extension of the non-conformable local fractional derivative, to the case of functions of several variables. Results analogous to those known from the classic multivariate calculus are presented. To show the strength of this approach, we show an extension of the Second Lyapunov Method to the non-conformable local fractio...
In this paper, using a generalized integral operator of the Riemann-Liouville type defined in a previous paper, we present several integral inequalities of Grüss type. Several existing results are obtained as the special cases of the results derived in this paper.
In this note we obtain sufficient conditions under which we can guarantee the stability of solutions of a fractional differential equations of non conformable type and we obtain some fractional analogous theorems of the direct Lyapunov method for a given class of equations of motion.
The present paper is the first of a series of works planned by the authors to study some qualitative properties of Liénard type equations solutions with derivatives of both natural and fractional order. In the present paper, we investigate the behaviour of limit cycles of the Biryukov equation, which is an important from the applicability standpoin...
This paper is concerned with random impulsive integro-differential equations with nonlocal conditions. At first, some sufficient conditions which can guarantee existence and uniqueness of mild solution are derived using Banach fixed point theorem. Secondly, combining with Banach fixed point theorem with some inequality techniques, we give stability...
Integrales de Línea. Integrales de Superficies. Fórmulas Integrales.
In this paper we present different variants of the well-known Hermite-Hadamard inequality , in a generalized context. We consider general fractional integral operators for h-convex and r-convex functions.
Teoremas de la Función Implícita Existencia unicidad,
continuidad, derivabilidad y diferenciabilidad de funciones
definidas en forma implícita Cambio de variables
La ecuación de ondas en una dimensión Problema de Cauchy
Fórmula de D Alembert Problema de tipo mixto Método de reflexión
Método de energía La ecuación de ondas en dimensiones superiores
In this work we show the historical significance of mathematical problems and their meaning, not only for Mathematics itself, but for the Philosophy of Mathematics and other related sciences, in which the current conceptual and methodological apparatus has been developed, as a result of the development of investigations related to the resolution of...
In this paper, we de�fine a new fractional integral operator, which we have called Generalized
k-Proportional Fractional Integral Operators with General Kernel, and its fundamental properties are studied, in addition it is shown that this operator contains, as a particular case, several of the known operators of the literature. Later, several integ...
En esta conferencia se presentan algunas de las características y funciones de la evaluación, previo a la pandemia. Sobre esta base y la experiencia acumulada, se brindan algunas recomendaciones de trabajo.
En esta conferencia, presentamos algunas de las direcciones de trabajo que pueden derivarse de la situación actual en que estamos viviendo, y que pueden ser utilizadas como recursos didácticos en el proceso de enseñanza-aprendizaje en la Educación Matemática de Nivel Superior. Ilustramos nuestra propuesta, dentro de la corriente matemática Realista...
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Projects (20)
We as a researcher, professor, scientists, experts, academics, scholars are always focused on the creation of current scientific discoveries and also enriched our research aspects with the latest developments in concerned disciplines to benifit the growth of our civilization and make it ease in every aspects and domains, thus establishing standards for the continuous progressions. Therefore, this project should be seen as a repository to incorporate new works where every scientists and scholars can view the works, recommends, cites of the other collaborators, to encourage and help each other for a more faster means of interdisciplinary communications through this interdisciplinary community to foster research on a global standards.
Considered the “Key to the Gulf of Mexico”, Cuba is the largest island country in the Caribbean sea, with a total area of almost 111 thousand square kilometers. The aim of this project is to promote the Cuban history, civilization, culture, gastronomy, natural landscapes and traditional folk music heritage.