Author
Stiven Díaz
Bio: Stiven Díaz is an academic researcher from Universidad del Norte, Colombia. The author has contributed to research in topics: Mathematics & Subordination (linguistics). The author has an hindex of 3, co-authored 5 publications receiving 11 citations.
Papers
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TL;DR: In this paper, the authors introduce the class of $(N, λ )$ -periodic vector-valued sequences and show several notable properties of this new class, including periodic, anti-periodic, Bloch and unbounded sequences.
Abstract: In this paper we introduce the class of $(N,\lambda )$
-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 $(N, \lambda )$
-periodic solutions to the following class of Volterra difference equations with infinite delay: $$ u(n+1)=\alpha \sum_{j=-\infty }^{n}a(n-j)u(j)+f \bigl(n,u(n) \bigr), \quad n \in \mathbb{Z}, \alpha \in \mathbb{C}, $$
where the kernel a and the nonlinear term f satisfy suitable conditions.
8 citations
TL;DR: In this article, the notion of Levy α-stable distribution within the discrete setting was introduced, and a subordination principle was proved, which relates a sequence of solution operat...
Abstract: In this paper, we introduce the notion of Levy α-stable distribution within the discrete setting. Using this notion, a subordination principle is proved, which relates a sequence of solution operat...
8 citations
TL;DR: An a posteriori error analysis of the two‐dimensional time‐dependent Stokes problem with homogeneous Dirichlet boundary conditions is conducted, which can be extended to mixed boundary conditions and an adaptive space/time mesh refinement strategy is developed.
5 citations
TL;DR: In this article , the authors established sufficient conditions for the existence and uniqueness of periodic solutions for the following abstract model: (n, λ)-periodic solutions for a closed linear operator defined in a Banach space X, where λ denotes the fractional difference operator in the Weyl-like sense.
Abstract: We establish sufficient conditions for the existence and uniqueness of $$(N,\lambda )$$ -periodic solutions for the following abstract model: $$\begin{aligned} \Delta ^{\alpha }u(n)=Au(n+1)+f(n,u(n)), \quad n\in {\mathbb {Z}}, \end{aligned}$$ where $$0 < \alpha \le 1 $$ , A is a closed linear operator defined in a Banach space X, $$\Delta ^{\alpha }$$ denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.
5 citations
TL;DR: The main objective of as discussed by the authors is to deduce some interesting algebraic relationships that connect the degenerated generalized generalized Apostol-Bernoulli, Euler and Genocchi polynomials.
Abstract: The main objective of this work is to deduce some interesting algebraic relationships that connect the degenerated generalized Apostol–Bernoulli, Apostol–Euler and Apostol– Genocchi polynomials and other families of polynomials such as the generalized Bernoulli polynomials of level m and the Genocchi polynomials. Futher, find new recurrence formulas for these three families of polynomials to study.
2 citations
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TL;DR: In this paper, a new class of non-instantaneous impulsive Cauchy matrices is studied and the existence and uniqueness of periodic solutions for nonlinear impulsive problems via fixed point theorems are established.
Abstract: In this paper, we study a new class of
$$(\omega , c)$$
-periodic non-instantaneous impulsive differential equations and we present new properties of the non-instantaneous impulsive Cauchy matrix. We establish existence and uniqueness of
$$(\omega ,c)$$
-periodic solutions for nonlinear impulsive problem via fixed point theorems. Examples are given to illustrate our theoretical results.
12 citations
TL;DR: In this article, the authors studied a class of periodic time varying impulsive differential equations and established the existence and uniqueness results for these equations for homogeneous and non-homogeneous problems.
Abstract: In this paper, we study a class of $(\omega ,c)$
-periodic time varying impulsive differential equations and establish the existence and uniqueness results for $(\omega ,c)$
-periodic solutions of homogeneous problem as well as nonhomogeneous problem.
9 citations
TL;DR: In this article , the authors established sufficient conditions for the existence and uniqueness of periodic solutions for the following abstract model: (n, λ)-periodic solutions for a closed linear operator defined in a Banach space X, where λ denotes the fractional difference operator in the Weyl-like sense.
Abstract: We establish sufficient conditions for the existence and uniqueness of $$(N,\lambda )$$ -periodic solutions for the following abstract model: $$\begin{aligned} \Delta ^{\alpha }u(n)=Au(n+1)+f(n,u(n)), \quad n\in {\mathbb {Z}}, \end{aligned}$$ where $$0 < \alpha \le 1 $$ , A is a closed linear operator defined in a Banach space X, $$\Delta ^{\alpha }$$ denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.
5 citations
TL;DR: In this article , the existence and uniqueness of (N, λ )-periodic solutions for the following abstract model were established: 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.
Abstract: . We establish sufficient conditions for the existence and uniqueness of ( N, λ )-periodic solutions for the following abstract model: 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.
4 citations