Jackie Harjani Sauco

Jackie Harjani Sauco
Universidad de Las Palmas de Gran Canaria | ULPGC · Department of Mathematics

About

45
Publications
3,357
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,437
Citations

Publications

Publications (45)
Article
Full-text available
We study the role of disorder in the vibration spectra of molecules and atoms in solids. This disorder may be described phenomenologically by a fractional generalization of ordinary quantum-mechanical oscillator problem. To be specific, this is accomplished by the introduction of a so-called fractional Laplacian (Riesz fractional derivative) to the...
Preprint
We study the role of disorder in the vibration spectra of molecules and atoms in solids. This disorder may be described phenomenologically by a fractional generalization of ordinary quantum-mechanical oscillator problem. To be specific, this is accomplished by the introduction of a so-called fractional Laplacian (Riesz fractional derivative) to the...
Article
In this paper, we present a result about the existence and uniqueness of positive solutions for a class of singular fractional differential equations with infinite-point boundary value conditions. The main tool used in the proof of the results is a fixed point theorem.
Article
Full-text available
In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its co...
Article
In this paper, we present a sufficient condition for the uniqueness of solutions to a nonlocal fractional boundaryvalue problem which can be considered as the fractional version to the thermostat model. As application of ourresult, we study the eigenvalues problem associated and, moreover, we get a Lyapunov-type inequality.
Article
Full-text available
In this paper, we prove a fixed point theorem for operators of Meir–Keeler type by using the concept of degree of nondensifiability. As an application of our result, we study the existence of solutions for a class of functional equations appearing in dynamic programming.
Article
Full-text available
Abstract In this paper, we derive some Hartman–Wintner type inequalities for a certain higher order fractional boundary value problem. As an application of our results, we obtain a lower bound for the eigenvalues of the corresponding fractional operator.
Article
In this paper, by using a recent fixed point theorem, we study the existence and uniqueness of positive solutions for the following m-point fractional boundary value problem on an infinite interval $$\begin{aligned} \left\{ \begin{array}{ll} D_{0^{+}}^{\alpha }x(t)+f(t,x(t))=0,&{}\quad 0<t<\infty ,\\ x(0)=x'(0)=0,&{}\quad D_{0^{+}}^{\alpha -1}x(+\i...
Article
Full-text available
In this paper, we prove the existence and uniqueness of solutions for the following fractional boundary value problem $$\begin{aligned} \left\{ \begin{aligned}&^cD_{0+}^\alpha u(t)=\lambda f(t,u(t)),\quad t\in [0,1],\\&u(0)=\gamma I_{0+}^\rho u(\eta )=\gamma \int _0^\eta \frac{(\eta -s)^{\rho -1}}{\Gamma (\rho )}u(s)\mathrm {d}s, \end{aligned} \rig...
Article
In this paper, we study sufficient conditions for the existence of positive solutions to a class of fractional differential equations of arbitrary order. Our solutions are placed in the space of Lipschitz functions and, perhaps, this is a part of the originality of the paper. For our study, we use a recent result about the relative compactness in H...
Chapter
The principal aim of this chapter is to consider the function space consisting of functions defined on a compact metric space with growths tempered by a given modulus of continuity and its connection with the measures of noncompactness. The chapter is inspired in the papers [1, 2].
Article
In this paper, we present a result about the existence of a generalized coupled fixed point in the space C[0; 1]. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in C[0; 1] for a general system of nonlinear functional-integral equations with maximum.
Article
In this paper, we introduce the definition of generalized coupled fixed point in the space of the bounded functions on a set S and we prove a result about the existence and uniqueness of such points. As an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations which ap...
Article
In this paper, we prove the existence and uniqueness of solutions for a coupled system of fractional differential equations with integral boundary conditions. Our analysis relies on a generalized coupled fixed point theorem in the space of the continuous functions defined on [0,1]. An example is also presented to illustrate the obtained results.
Article
In this paper, we present a result about the existence of a generalized coupled fixed point in the space C[0; 1]. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in C[0; 1] for a general system of nonlinear functional-integral equations with maximum.
Article
The purpose of this paper is provide sufficient conditions for the existence of a unique best proximity point for contractions of Geraghty type. Our paper improves a recent result due to Caballero et al. (Fixed Point Theory and Applications. doi:10.1186/1687-1812-2012-231, 2012).
Article
Full-text available
We introduce the definition of α-coupled fixed point in the space of the bounded functions on a set S and we present a result about the existence and uniqueness of such points. Moreover, as an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic pr...
Article
The purpose of this paper is to provide sufficient conditions for the existence of a unique best proximity point for generalized weakly contractive mappings in the context of complete metric spaces.
Article
The purpose of this paper is to present a fixed point theorem for cyclic weak contractions in compact metric spaces.
Article
Full-text available
The purpose of this paper is to present a fixed point theorem due to Dass and Gupta (Indian J Pure Appl Math 6:1455–1458, 1975) in the context of partially ordered metric spaces.
Article
The purpose of this paper is to present a fixed point theorem for monotone generalized contractions satisfying a contractive condition of rational type in the context of partially ordered metric spaces. Our results extend other recent results.
Article
The purpose of this paper is to present some fixed point results for mappings of cyclical type in the context of ordered metric spaces. Our results extend the ones in [A. Amini-Harandi and H. Emami, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 5, 2238–2242 (2010; Zbl 1197.54054)].
Article
The purpose of this paper is to present some fixed point results for cyclic weak contractions in partially ordered sets endowed with a complete metric.
Article
The purpose of this paper is to present some fixed point results for cyclic φ-contractions in a complete metric space endowed with a partial order.
Article
Full-text available
The purpose of this paper is to provide sufficient conditions for the existence of a unique best proximity point for Geraghty-contractions. Our paper provides an extension of a result due to Geraghty (Proc. Am. Math. Soc. 40:604-608, 1973).
Article
Full-text available
We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0, 0 < t < 1 , u ( 0 ) = u ′ ( 0 ) = u ′′ ( 0 ) = 0 , u ′′ ( 1 ) = β u ′′ ( η ) , where 3 < α ≤ 4 , D 0 + α is the standard Riemann-Liouville derivative and f : ( 0,1 ] × [...
Article
Full-text available
We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D0+αu(t)+f(t,u(t))=0, 0<t<1, 2<α≤3, u(0)=u'(0)=0, u'(1)=∑i=1m-2aiu'(ξi), where D0+α denotes the standard Riemann-Liouville fractional derivative, f:[0,1]×[0,∞)→[0,∞) is a continuous funct...
Article
The purpose of this paper is to present some fixed point theorems for monotone generalized contractions in a complete metric space endowed with a partial order. Some results appearing in [9] and in [12] can be obtained as particular cases of our theorems. An application to integral equations is presented in order to illustrate our results.
Article
Full-text available
The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem where 2 < α ≤ 3 and is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in...
Article
Full-text available
The purpose of this paper is to present some fixed point theorems for Meir-Keeler contractions in a complete metric space endowed with a partial order. MSC: 47H10.
Article
In this paper, we investigate the existence and uniqueness of positive solutions for the following singular fractional boundary value problem D0+αu(t)+f(t,u(t))=0,0<t<1,u(0)=u(1)=0, where 1<α≤21<α≤2, D0+α is the standard Riemann–Liouville differentiation and f:(0,1]×[0,∞)⟶[0,∞)f:(0,1]×[0,∞)⟶[0,∞) with limt→0+f(t,−)=∞limt→0+f(t,−)=∞ (i.e., ff is sin...
Article
The purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions. We also present an application to integral equations.
Article
The purpose of this paper is to present some fixed point results for weakly C-contractive mappings in a complete metric space endowed with a partial order.
Article
Full-text available
We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: ${D}_{0+}^{\alpha }u(t)+f(t,u(t))=0$ , $0\le t\le 1$, $3\lt \alpha \le 4$, $u(0)={u}^{\prime }(0)={u}^{″}(0)={u}^{″}(1)=0$, where ${D}_{0+}^{\alpha }$ denotes the standard Riemann-Liouville fractional derivative. O...
Article
Full-text available
The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem: y(4)(t)=f(t,y(t)), t∈[0,1], y(0)=y(1)=y′(0)=y′(1)=0. Moreover, under certain assumptions, we will prove that the above boundary value problem has a unique symmetric positive solution. Finally, we pres...
Article
This work presents sufficient conditions for the existence and uniqueness of a positive solution for a nonlinear fourth-order differential equation under Lidstone boundary conditions. Our analysis relies on a fixed point theorem in partially ordered sets. KeywordsFourth-order boundary value problem-Partially ordered set-Fixed point theorem-Positiv...
Article
This paper presents sufficient conditions for the existence and uniqueness of a positive solution to a nonlinear fourth-order differential equation under Lidstone boundary conditions Our analysis relies on a fixed point theorem in partially ordered sets
Article
The purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions. We also present some applications to first and second order ordinary differential equations.
Article
Full-text available
The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.
Article
Full-text available
The purpose of this paper is to present a fixed point theorem using a contractive condition of rational type in the context of partially ordered metric spaces.
Article
The purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order.
Article
Full-text available
We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.
Article
Full-text available
The main aim of this paper is to study the existence of solutions of the following recursive functional equation x(n) = f(n, x(n), x(n - 1)) in the space l2, under general assumptions. The main tools of our existence theorem are the characterization of the relatively compact sets in the space l2 and Schauder Fixed point theorem. Moreover, our funct...