Stiven Diaz Noguera | Universidad de la Costa (original) (raw)

Papers by Stiven Diaz Noguera

We show maximal regularity estimates for the damped hyperbolic and strongly damped wave equations... more We show maximal regularity estimates for the damped hyperbolic and strongly damped wave equations with periodic initial conditions in a cylindrical domain. We prove that this property strongly depends on a critical combination on the parameters of the equation. Noteworthy, our results are still valid for fractional powers of the negative Laplacian operator. We base our methods on the theory of operator-valued Fourier multipliers on vector-valued Lebesgue spaces of periodic functions.

This work primarily focuses on (N,λ)-periodic sequences and their applications. To begin, we prov... more This work primarily focuses on (N,λ)-periodic sequences and their applications. To begin, we provide a brief overview of (N,λ)-periodic sequences and introduce several results. Secondly, in terms of applications and main objective, we establish sufficient criteria for both the existence and uniqueness of (N,λ)-periodic mild solutions for abstract difference equations of convolution type. Furthermore, we present illustrative examples to highlight our key findings.

Axioms

In this paper, we introduce a class of new classes of degenerate unified polynomials and we show ... more In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations. Most of the results are proved by using generating function methods and we illustrate our results with some examples.

This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–... more This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials of level m. We establish some algebraic and differential properties for generalizations of new classes of degenerated Apostol–Bernoulli polynomials. These results are shown using generating function methods for Apostol–Euler and Apostol–Genocchi Hermite polynomials of level m.

In this paper, we investigate the existence and uniqueness of (ω,Q)-periodic mild solutions for t... more In this paper, we investigate the existence and uniqueness of (ω,Q)-periodic mild solutions for the following problem
x′(t)=Ax(t)+f(t,x(t)),t∈R,
on a Banach space X. Here, A is a closed linear operator which generates an exponentially stable C0-semigroup and the nonlinearity f satisfies suitable properties. The approaches are based on the well-known Banach contraction principle. In addition, a sufficient criterion is established for the existence and uniqueness of (ω,Q)-periodic mild solutions to the Hopfield-type neural network model.

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Welcome to Manizales 2022! We are delighted to welcome friends and colleagues to our home city of... more Welcome to Manizales 2022! We are delighted to welcome friends and colleagues to our home city of Manizales for the XV GAFEVOL Congress 2022. Continuing the successful trend of past Congresses, the 2022 Congress in Manizales shows how important the GAFEVOL Congress has become as a regular platform accommodating the rapid pace of progress in the Evolution Equations and Functional Analysis field and for presenting the results of studies which have a direct impact on the applications. GAFEVOL 2022 will provide a Scientific Programme that builds on the highly successful models from previous Congresses, while incorporating innovative suggestions from valuable stakeholders. This Congress will feature presentations of some of the most recent research including observability of certain types of equations, time scales, Fourier multipliers systems, analyticity of semigroups, Schrödigner type equations, controllability of systems, chaotic dynamics of non local models, advances on existence, periodicity, mild solutions, classical solutions, extensions, global bifurcation, and convergence of solutions for different classes of ODE's and PDE's. Also, applications to Covid 19 will be treated.

WSEAS transactions on mathematics, Aug 5, 2022

Mediterranean Journal of Mathematics, 2022

Journal of Mathematical Analysis and Applications, 2022

The main goal in this paper is to study asymptotic behaviour in L p (R N) for the solutions of th... more The main goal in this paper is to study asymptotic behaviour in L p (R N) for the solutions of the fractional version of the discrete in time N-dimensional diffusion equation, which involves the Caputo fractional h-difference operator. The techniques to prove the results are based in new subordination formulas involving the discrete in time Gaussian kernel, and which are defined via an analogue in discrete time setting of the scaled Wright functions. Moreover, we get an equivalent representation of that subordination formula by Fox H-functions.

Communications in Contemporary Mathematics, 2020

In this paper, we introduce the notion of Lévy [Formula: see text]-stable distribution within the... more In this paper, we introduce the notion of Lévy [Formula: see text]-stable distribution within the discrete setting. Using this notion, a subordination principle is proved, which relates a sequence of solution operators — given by a discrete [Formula: see text]-semigroup — for the abstract Cauchy problem of first order in discrete-time, with a sequence of solution operators for the abstract Cauchy problem of fractional order [Formula: see text] in discrete-time. As an application, we establish the explicit solution of the abstract Cauchy problem in discrete-time that involves the Hilfer fractional difference operator and prove that, in some cases, such solution converges to zero. Our findings give new insights on the theory, provide original concepts and extend as well as improve recent results of relevant references on the subject.

Advances in Difference Equations, 2019

In this paper we introduce the class of (N, λ)-periodic vector-valued sequences and show several ... more In this paper we introduce the class of (N, λ)-periodic vector-valued sequences and show several notable properties of this new class. This class includes periodic, anti-periodic, Bloch and unbounded sequences. Furthermore, we show the existence and uniqueness of (N, λ)-periodic solutions to the following class of Volterra difference equations with infinite delay: u(n + 1) = α n j=-∞ a(n-j)u(j) + f (n, u(n)), n ∈ Z, α ∈ C, where the kernel a and the nonlinear term f satisfy suitable conditions.

Numerical Methods for Partial Differential Equations, 2018

We establish sufficient conditions for the existence and uniqueness of (N,λ)-periodic solutions f... more We establish sufficient conditions for the existence and uniqueness of (N,λ)-periodic solutions for the following abstract model:

Δ^α u(n)=Au(n+1)+f(n,u(n)), n∈Z,

where 0<α≤1, A is a closed linear operator defined in a Banach space X, Δ^α denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.

The main goal in this paper is to study asymptotic behavior in L p (R N) for the solutions of the... more The main goal in this paper is to study asymptotic behavior in L p (R N) for the solutions of the fractional version of the discrete in time N-dimensional diffusion equation, which involves the Caputo fractional h-difference operator. The techniques to prove the results are based in new subordination formulas involving the discrete in time Gaussian kernel, and which are defined via an analogue in discrete time setting of the scaled Wright functions. Moreover, we get an equivalent representation of that subordination formula by Fox H-functions.

In this article we show you the results of an investigation with high school students in order to... more In this article we show you the results of an investigation with high school students in order to evaluate their attitudes in math and their academic performance. The analisis of the results reveals that the attitudes and the academic performance are correlated and influence each other.

Talks by Stiven Diaz Noguera

Drafts by Stiven Diaz Noguera

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

We show maximal regularity estimates for the damped hyperbolic and strongly damped wave equations... more We show maximal regularity estimates for the damped hyperbolic and strongly damped wave equations with periodic initial conditions in a cylindrical domain. We prove that this property strongly depends on a critical combination on the parameters of the equation. Noteworthy, our results are still valid for fractional powers of the negative Laplacian operator. We base our methods on the theory of operator-valued Fourier multipliers on vector-valued Lebesgue spaces of periodic functions.

This work primarily focuses on (N,λ)-periodic sequences and their applications. To begin, we prov... more This work primarily focuses on (N,λ)-periodic sequences and their applications. To begin, we provide a brief overview of (N,λ)-periodic sequences and introduce several results. Secondly, in terms of applications and main objective, we establish sufficient criteria for both the existence and uniqueness of (N,λ)-periodic mild solutions for abstract difference equations of convolution type. Furthermore, we present illustrative examples to highlight our key findings.

Axioms

In this paper, we introduce a class of new classes of degenerate unified polynomials and we show ... more In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations. Most of the results are proved by using generating function methods and we illustrate our results with some examples.

This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–... more This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials of level m. We establish some algebraic and differential properties for generalizations of new classes of degenerated Apostol–Bernoulli polynomials. These results are shown using generating function methods for Apostol–Euler and Apostol–Genocchi Hermite polynomials of level m.

In this paper, we investigate the existence and uniqueness of (ω,Q)-periodic mild solutions for t... more In this paper, we investigate the existence and uniqueness of (ω,Q)-periodic mild solutions for the following problem
x′(t)=Ax(t)+f(t,x(t)),t∈R,
on a Banach space X. Here, A is a closed linear operator which generates an exponentially stable C0-semigroup and the nonlinearity f satisfies suitable properties. The approaches are based on the well-known Banach contraction principle. In addition, a sufficient criterion is established for the existence and uniqueness of (ω,Q)-periodic mild solutions to the Hopfield-type neural network model.

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Welcome to Manizales 2022! We are delighted to welcome friends and colleagues to our home city of... more Welcome to Manizales 2022! We are delighted to welcome friends and colleagues to our home city of Manizales for the XV GAFEVOL Congress 2022. Continuing the successful trend of past Congresses, the 2022 Congress in Manizales shows how important the GAFEVOL Congress has become as a regular platform accommodating the rapid pace of progress in the Evolution Equations and Functional Analysis field and for presenting the results of studies which have a direct impact on the applications. GAFEVOL 2022 will provide a Scientific Programme that builds on the highly successful models from previous Congresses, while incorporating innovative suggestions from valuable stakeholders. This Congress will feature presentations of some of the most recent research including observability of certain types of equations, time scales, Fourier multipliers systems, analyticity of semigroups, Schrödigner type equations, controllability of systems, chaotic dynamics of non local models, advances on existence, periodicity, mild solutions, classical solutions, extensions, global bifurcation, and convergence of solutions for different classes of ODE's and PDE's. Also, applications to Covid 19 will be treated.

WSEAS transactions on mathematics, Aug 5, 2022

Mediterranean Journal of Mathematics, 2022

Journal of Mathematical Analysis and Applications, 2022

The main goal in this paper is to study asymptotic behaviour in L p (R N) for the solutions of th... more The main goal in this paper is to study asymptotic behaviour in L p (R N) for the solutions of the fractional version of the discrete in time N-dimensional diffusion equation, which involves the Caputo fractional h-difference operator. The techniques to prove the results are based in new subordination formulas involving the discrete in time Gaussian kernel, and which are defined via an analogue in discrete time setting of the scaled Wright functions. Moreover, we get an equivalent representation of that subordination formula by Fox H-functions.

Communications in Contemporary Mathematics, 2020

In this paper, we introduce the notion of Lévy [Formula: see text]-stable distribution within the... more In this paper, we introduce the notion of Lévy [Formula: see text]-stable distribution within the discrete setting. Using this notion, a subordination principle is proved, which relates a sequence of solution operators — given by a discrete [Formula: see text]-semigroup — for the abstract Cauchy problem of first order in discrete-time, with a sequence of solution operators for the abstract Cauchy problem of fractional order [Formula: see text] in discrete-time. As an application, we establish the explicit solution of the abstract Cauchy problem in discrete-time that involves the Hilfer fractional difference operator and prove that, in some cases, such solution converges to zero. Our findings give new insights on the theory, provide original concepts and extend as well as improve recent results of relevant references on the subject.

Advances in Difference Equations, 2019

In this paper we introduce the class of (N, λ)-periodic vector-valued sequences and show several ... more In this paper we introduce the class of (N, λ)-periodic vector-valued sequences and show several notable properties of this new class. This class includes periodic, anti-periodic, Bloch and unbounded sequences. Furthermore, we show the existence and uniqueness of (N, λ)-periodic solutions to the following class of Volterra difference equations with infinite delay: u(n + 1) = α n j=-∞ a(n-j)u(j) + f (n, u(n)), n ∈ Z, α ∈ C, where the kernel a and the nonlinear term f satisfy suitable conditions.

Numerical Methods for Partial Differential Equations, 2018

We establish sufficient conditions for the existence and uniqueness of (N,λ)-periodic solutions f... more We establish sufficient conditions for the existence and uniqueness of (N,λ)-periodic solutions for the following abstract model:

Δ^α u(n)=Au(n+1)+f(n,u(n)), n∈Z,

where 0<α≤1, A is a closed linear operator defined in a Banach space X, Δ^α denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.

The main goal in this paper is to study asymptotic behavior in L p (R N) for the solutions of the... more The main goal in this paper is to study asymptotic behavior in L p (R N) for the solutions of the fractional version of the discrete in time N-dimensional diffusion equation, which involves the Caputo fractional h-difference operator. The techniques to prove the results are based in new subordination formulas involving the discrete in time Gaussian kernel, and which are defined via an analogue in discrete time setting of the scaled Wright functions. Moreover, we get an equivalent representation of that subordination formula by Fox H-functions.

In this article we show you the results of an investigation with high school students in order to... more In this article we show you the results of an investigation with high school students in order to evaluate their attitudes in math and their academic performance. The analisis of the results reveals that the attitudes and the academic performance are correlated and influence each other.

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY