Juan Eduardo Nápoles Valdes

National University of the Northeast | UNNE · Department of Mathematics (Faculty of Natural and Exact Sciences and Surveying)

In this work we present a new definition of local derivative, with good properties, which is a natural generalization of the classical derivative. The main novelty is that this derivative allows us to expand the class of continuous functions and differentiable functions, one of the most requested issues in the definition of new differential operato...

This project is dedicated to fractional calculus, one of the most dynamic areas of mathematical science today. For 50 years, the number of researchers and scientific publications dealing with this topic has been increasing day by day, which clearly demonstrates the growing interest in fractional calculus, both from a practical and a theoretical poi...

The harmonic polynomial was defined in order to understand better the harmonic topological index. Here, we obtain several properties of this polynomial, and we prove that several properties of a graph can be deduced from its harmonic polynomial. Also, we prove that graphs with the same harmonic polynomial share many properties although they are not...

In this work we obtain integral inequalities of the Hermite-Hadamard type, using generalized derivatives of the Caputo type. Throughout the work, we see that several results reported in the literature are particular cases of those presented here.

This Special Issue of the scientific journal Axioms, entitled “Recent Advances in Fractional Calculus”, is dedicated to one of the most dynamic areas of mathematical sciences today [...]

This event offers an ideal forum for curious people from Mexico and worldwide to present their latest research in Fractional Calculus.

New variants of the Hermite-Hadamard inequality within the framework of generalized fractional integrals for (h, m, s)-convex modified second type functions have been obtained in this article. To achieve these results, we used the Holder inequality and another form of it-power means. Some of the known results described in the literature can be cons...

We obtain several new integral inequalities in terms of fractional integral operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the results obtained provide better upper estimates than those known in the literature for Bullen-type inequality and...

Resumen de la charla: En esta exposición se presentarán algunos resultados clásicos relacionados con la Desigualdad de Hermite-Hadamard y se esbozarán las cuatro líneas de investigación actuales vinculados a este desarrollo: 1) con nuevas nociones de convexidad, 2) refinando la "malla" usada, 3) usando diversos funcionales para acotar el miembro iz...

This article explores the mechanical analysis of a unified chaotic system and matrix projective synchronization (MPS). The sufficient conditions to achieve MPS of unified chaotic system have derived. The mechanics of unified chaotic system have been examined in contrast with Kolmogorov system, Euler equation, and Hamiltonian function. The Casimir e...

In this paper, we introduce the Ω-derivative, which generalizes the classical concept of derivative. Main properties of this new derivative are revised. We also study Ω-differential equations and some of its applications.

In this article, we establish some new generalized inequalities of the Hilbert-type on time scales’ delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dynamic inequalities of the Hilbert-type on time scales’ delta calculus for delta differentiable functions o...

In this note we present some numerical simulations of the asymptotic behavior of a Generalized Liénard Equation, taking into account a recently defined differential operator. We must point out that these numerical variations have not been obtained as usual: by varying the functions of the right member of the system considered, but, on the contrary,...

In this paper, we consider general convex functions of various type. We establish some new integral inequalities of Hermite-Hadamard type for (h, s, m)-convex and (h, m)-convex functions, using generalized integrals. We also investigate differentiable functions with general convex derivative. The proven results generalize many results previously kn...

In this paper, we obtain new inequalities of the Hermite-Hadamard type, in two different classes of convex dominated functions. Several known results from the literature are obtained as particular cases of our more general perspective. Resumen. En este artículo, obtenemos nuevas desigualdades del tipo Hermite-Hadamard, en dos clases diferentes de f...

In this work we establish a Simpson-type identity and several Simpson-type inequalities for generalized weighted integrals operators. Key words and phrases. Simpson integral inequality, integral operators weighted, (α, m)-convex functions. 2010 Mathematics Subject Classification. 26D15, 26D10, 41A55. Resumen. En este trabajo establecemos una identi...

In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite–Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann–Liouville and the $ k $-Riemann–Liouville fractional integral operators. The functions for which the operators were considered sat...

As timely renovation of humanistic 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 in logic enantiomorph of newly highlighted factuality of discretionary pa...

In this study, we provide a conformable fractional calculus generalization of the density of various functional spaces, such as spaces of continuous functions, spaces of order α derivatives, fractional spaces of Lebesgue integrals, and fractional Sobolev's spaces.

In this article, we establish some new generalized inequalities of Hilbert-type on time scales delta calculus which considered as similar formulas for inequalities of Hilbert type proved by Chang-Jian, Lian-Ying and Cheung [7]. These inequalities will proved by applying Hölder’s inequality, chain rule on time scales and the mean inequality. As spec...

In this note, starting with a lemma, we obtain several extensions of the well-known Hermite-Hadamard inequality for convex functions, using generalized weighted integral operators.

"In this paper, using a generalized operator of the Riemann-Liouville type, defined and studied in a previous work, several integral inequalities for synchronous functions are established."

For all convex functions, the Hermite–Hadamard inequality is already well known in convex analysis. In this regard, Hermite–Hadamard and Ostrowski type inequalities were obtained using exponential type convex functions in this work. In addition, new generalizations were found for different values of θ. In conclusion, we believe that our work’s tech...

Water" is nothing but a just word, it is the world priciest required because no one can live without water and in just a this whole world, 70% of the surface is occupied with water. This shows that not only the living things even the world is adherent to water so, In my essay "SCIENTIFIC APPROACH OF WATER MANAGEMENT IN TAMIL SOCIETY". I Put forth v...

We obtain a general solution of the 2-variable quadratic functional equation ζ(y1+y2,y3+y4)+ζ(y1-y2,y3-y4)=2ζ(y1,y3)+2ζ(y2,y4) and discuss the stability of the above functional equation, while the quadratic form ζ(a,b)=αa2+βab+γc2 is a solution of our functional equation. Keywords: Fuzzy normed space, Fixed point, Fuzzy stability, τ-norm, quadr...

This article presents new developments and applications of Jensen's inequality. We explore various variations of Jensen's inequality related to modified (h, m)-convex functions. The obtained results extend the applicability of the inequality to a broader class of functions and contexts. In addition to the fact that the results presented in the arti...

In this work we present a review of the known main generalized derivatives.

In this paper, we use the k-generalized fractional Riemann-Liouville integral of order α to obtain new integral inequalities of the Hermite-Hadamard type, in the class of P −functions.

In this paper, we present a general formulation of the Riemann–Liouville fractional operator with generalized kernels. Many of the known operators are shown to be particular cases of the one we present. In this new framework, we prove several known integral inequalities in the literature

In this paper we propose and solve a generalization of the Bernoulli Differential Equation, by means of a generalized fractional derivative. First we prove a generalization of Gronwall's inequality, which is useful for studying the stability of systems of fractional differential equations and we state results about the qualitative behavior of the t...

Some new results related to generalized Hermite-Hadamard-type inequalities are established. For obtaining new inequalities , various approaches are utilized, including boundedness, convexity, and concavity. Considering special values of the parameters, it is demonstrated how the obtained inequalities reduce to the known ones.

By means of Caputo k−fractional derivatives, in this work, we obtain new extensions of the Hermite-Hadamard inequality for modified (h, m)− convex functions of the second type. At work, we show that some known results from the literature can be obtained as particular cases of the results presented here.

By using the definition of modified (h, m)-convex functions of the second type, we present various refinements of the classical Hermite-Hadamard inequality obtained within the framework of weighted integrals. Throughout the paper, we show that various known results available from the literature can be obtained as particular cases of our results. За...

In this paper, we define a generalized fractional integral of order α which are the natural extension of the newly defined k-fractional conformable integrals and they can be reduced to other fractional integrals. Later, the existence of such k-generalized integrals is proved. Finally, discuses some future possibilities.

In this paper, we present some new integral inequalities of Hermite-Hadamard type. To obtain these results, general convex functions of various type are considered such as $(h,m)$-convex functions. The main results extend some previously known inequalities by taking fractional integral operators.

In this paper, we present generalized versions of the Wirtinger inequality , which contains as particular cases many of the well-known versions of this classic isoperimetric inequality. Some applications and open problems are also presented in the work. Mathematics Subject Classification (2010): 26A33, 26Dxx, 35A23.

In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen–Mercer inequality and its variants f...

In this work, we use weighted integrals to obtain new integral inequalities of the Simpson type for the class of pℎ, , qć onvex functions of the second type. In the work we show that the obtained results include some known from the literature, as particular cases.

In this Chapter, we established some new Ostrowski type inequalities via conformable fractional calculus by introducing a parameter. We also introduce a Mongomery identity, via a parameter, is useful for generalizations of Ostrowski’s inequality. Some results in the literature are particular cases of someof our results.

En esta conferencia, presentamos los últimos desarrollos obtenidos alrededor de esta clásica Desigualdad Integral y como, similar al mítico problema, un simple trozo de cuero de toro ha logrado cubrir una extensa área en las Ciencias Matemáticas de la actualidad.

The present work is related to a certain extension of intuitionist fuzzy sets, endowed with an addition operation, a scalar product, and a preorder relation. We show that this structure is a bounded left R 0-semimodule. We also discuss some metric properties and develop a new approach to the concept of mean, the application of which is illustrated...

In this article, several new integral inequalities were obtained in terms of fractional integral operators for the functions whose first derivatives satisfy the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, these inequalities give better upper bounds for the Hadamard-type trapezoidal inequality and Bullen ine...

A fractional order COVID-19 model consisting of six compartments in Caputo sense is constructed. The indirect transmission of the virus through susceptible populations by the shedding effect is studied. Equilibrium solutions are calculated, and basic reproduction ratio (that depends both on direct and indirect mode of transmission), existence and u...

In this paper, we give a brief summary of fractal calculus. Fractal functional differential equations are formulated as a framework that provides a mathematical model for the phenomena with fractal time and fractal structure. Fractal retarded, neutral, and renewal delay differential equations with constant coefficients are solved by the method of s...

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...

The aim of the paper is to present an analysis of special random impulsive fractional differential equations involving Fredholm and Volterra integrals. This paper is mainly focused to the existence, uniqueness and stability of special random impulsive fractional differential equations with local initial conditions and nonlocal initial conditions se...

Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index of the main products of graphs. Here, we obtain several properties of this polynomial, and we prove that several properties of graphs can be deduced from their harmonic p...

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 this paper, some new integral inequalities of the Hermite–Hadamard type are were obtained for (h,m)-convex modified functions. The results are obtained on the basis of the introduced definition of a generalized weighted integral operator by using the convexity property, the well-known Holder’s inequality and its modification. Some results existi...

In this paper, using the definition of functions (h, m, s)-convex modified of second type, various extensions of the classic Hermite-Hadamard Inequality are obtained using Katugampola integrals. In addition, we show that several results known are particular cases of ours.

In this work we present the main properties of the Generalized Laplace Transform, recently defined, and we show some applications. Laplace’s transformation has been very useful in the studies of engineering, mathematics, physics, among other scientific areas. One of the main mathematical areas where it has many applications is in the topic of diffe...

In this article, we establish several inequalities for (h, m)-convex maps, related to weighted integrals, used in previous works. Throughout the work, we show that our results generalize several of the integral inequalities known from the literature.

In this work, using weighted integrals, we obtain new integral inequalities of the Simpson-Mercer type for the class of (h, m)-convex functions of second type. Throughout the work it is shown that the results obtained contain as particular cases, several known from the literature.

In this work using k -fractional Caputo derivatives we obtain some versions of the Hadamard inequality for the function f such that f(n) is (h,m)-convex modified of the second type. Throughout the work, we show that some known results from the literature can be obtained as particular cases of the results presented here.

In this paper, we present some historical notes to Generalized Calculus, sometimes called Local Fractional Calculus, and highlight some properties and applications of these new mathematical tools.

In this paper, we consider a non-linear fractional diffusion-like equation. The existence and uniqueness of the solution of this type of equation are investigated. After that we use the homotopy perturbation method (HPM) to solve this equation by approximating a nonlinear function in a Taylor’s series form and obtain an approximate solution. © 2022...

In this work we present a generalized multi-index derivative, which contains as particular cases, with an index, several local derivatives known from the literature (both conformable and non-conformable). Obviously this new development contains many of the desirable properties of integer derivatives. It is worth noting that the multi-index differen...

Partners Universal International Research Journal ( PUIRJ) December 2022

This article is aimed at establishing some results concerning integral inequalities of the Opial type in the fractional calculus scenario. Specifically, a generalized definition of a fractional integral operator is introduced from a new Raina-type special function, and with certain results proposed in previous publications and the choice of the par...

In this work, we obtain new versions of the Hermite-Hadamard Inequality via generalized fractional derivatives, which differentiates our work from previous known ones, which use integral operators. Several known results from the literature are particular cases of ours, demonstrating the breadth and generality of our conclusions.

In this paper we establish various integral inequalities of Hermite-Hadamard type in the class of (h, m)-convex, recently defined in [4], for a broader idea on the development of the notion of convexity, we recommend [29]. Different versions of such inequalities are obtained, containing as special cases several results known from the literature, to...

In the present study, several new generalized integral inequalities of the Hadamard and Simpson-type are obtained. The results were obtained for functions whose first and third derivatives are either convex or satisfy the Lipschitz condition or the conditions of the Lagrange theorem. In a particular case, these results not only confirm but also imp...

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 research, we used a generalized fractional integral to create a new Hermite–Hadamard-type integral inequality for functions of two independent variables that are quasi-convex on the coordinates. We also introduce additional inequalities of the Hermite–Hadamard type for functions of two variables that are twice partially differentiable and w...

This work presents some asymptotic properties of the solutions, mainly related to the boundedness, of certain functional differential equations in the framework of the generalized local derivative.

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.

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...

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...

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.