# Jackie Harjani SaucoUniversidad de Las Palmas de Gran Canaria | ULPGC · Department of Mathematics

Jackie Harjani Sauco

## About

45

Publications

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## Publications

Publications (45)

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...

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...

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.

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...

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.

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.

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.

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...

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...

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...

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].

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.

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...

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.

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.

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).

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...

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.

The purpose of this paper is to present a fixed point theorem for cyclic weak contractions in compact metric spaces.

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.

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.

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)].

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.

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.

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).

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 ] × [...

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...

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.

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...

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.

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...

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.

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.

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...

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...

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...

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

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.

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.

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.

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.

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.

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...