Juan Rocha

• Dr.
• University of Las Palmas de Gran Canaria

The time-fractional porous medium equation is an important model of many hydrological, physical, and chemical flows. We study its self-similar solutions, which make up the profiles of many important experimentally measured situations. We prove that there is a unique solution to the general initial-boundary value problem in the one-dimensional setti...

From a fixed point theorists’ view, Hutchinson considered a fractal set as a fixed point problem and applied the Banach contraction principle to prove its existence. In this paper, we present a result about the existence of fractal for a finite iterated condensing function using the degree of nondensifiability.

In this paper, we focus on an integral equation which allows us to model the dynamics of the capillary rise of a fluid inside a tubular column. Using Schauder's fixed-point theorem, we prove that such integral equation has at least one solution in the Hölder space H1[0,b], where b>0. Moreover, we are able to prove the uniqueness of the solution und...

In this paper, we study the existence of positive solutions for a nonlocal fractional boundary value problem which can be considered as the fractional analog of the thermostat model. Our solutions are placed in the space of Hölder functions and the main tools used in the proof of the results are a sufficient condition about the relative compactness...

In this paper, we present a Lyapunov type inequality for a nonlinear fractional hybrid boundary value problem. We illustrate the main result through a series of examples.

In this paper, Lyapunov‐type inequalities are derived for a class of fractional boundary value problems with integral boundary conditions. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.

In this paper, we use the mixed monotone operator method to study the following nonlinear boundary value problem $$\begin{aligned} \left\{ \begin{array}{ll} -u'''(t)=f(t,u(t),u(\varrho t))+g(t,u(t)),&{}\quad 0<t<1,\,\varrho \in (0,1), \\ u(0)=u''(0)=u(1)=0. \end{array} \right. \end{aligned}$$An example is provided to illustrate the results.

Final outcome of raptors admitted to the Tafira Wildlife Rehabilitation Center, Gran Canaria Island, Spain (2003-2013).— The outcomes of wild raptors admitted to the Tafira Wildlife Rehabilitation Center in Gran Canaria Island, Spain, from 2003 to 2013 were analyzed using a quality auditing system based on the crude and stratified (by causes of adm...

The Strategic Partnership for the Development of Training Workshops and Modeling Clinic for In- dustrial Mathematics (acronym MODCLIM) is a strategic partnership for higher education project, approved in 2014 by Erasmus+ program, Key Action 2: Cooperation for innovation and the exchange of good practices. MODCLIM develops a project focused on math...

In this paper, we present some Lyapunov-type inequalities for a nonlinear fractional heat equation with nonlocal boundary conditions depending on a positive parameter. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.

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.

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...

We prove the existence of the PPF dependent fixed point in the Razumikhin class for contractions of rational type in Banach spaces, by using a general class of pairs of functions. Our result has as particular cases a great number of interesting consequences which extend and generalize some results appearing in the literature.

We study the solvability of a nonlinear quadratic integral equation of Hammerstein type. Using the technique of measures of noncompactness we prove that this equation has solutions on an unbounded interval. Moreover, we also obtain an asymptotic characterization of these solutions. Several special cases of this integral equation are discussed and a...

The aim of this paper is to obtain monotonic solutions of an integral equation of Volterra–Stieltjes type in C [0, 1]. Existence will be established with the aid of a measures of noncompactness. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Using a technique associated with measures of noncompactness we prove the existence of nondecreasing solutions for an integral equation in C[0,1].

Using the technique associated with measures of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

Using the. technique associated with some measures of noncompactness we prove the existence of monotonic solutions of some nonlinear integral equations. Measures of noncompactness used in our investigations are related to the monotonicity of functions defined and continuous on a real segment.

We study the solvability of the Goursat problem for the nonlinear hyperbolic partial differential equation in unbounded regions. The method of the proof of the main result depends on the construction of a special Banach space consisting of real functions being defined, continuous and tempered on a real half-axis and on applying the Schauder fixed p...

Using a technique associated with measures of noncompactness we prove the existence of nondecreasing solutions to integral equations of Volterra type in C[0,1].

The aim of this paper is to investigate a class of integral equation of Volterra type and its solvability in the space of continuous and bounded functions on . The main tool used in our considerations is the technique associated with measures of noncompactness.

Using the technique associated with measures of noncompactness we prove the existence of monotonic solutions of an integral equation related with the Chandrasekhar equation in the sense that their integral kernels coincide.

Dans cet article, nous etudions les submersions metriques presque contact a espace total une variete localement conformement cosymplectique. Nous obtenons des resultats sur la minimalite des fibres sur le transfert a la base de la structure metrique presque contact, sur la structure induite sur les fibres et finalement sur l'integrabilite de la dis...

In this paper we study almost Hermitian submersions with total space a locally conformal Khler (l.c.K.) manifold, i.e., l.c.K. submersions. We derive necessary and sufficient conditions for the fibers of a l.c.K. submersion to be minimal and for the horizontal distribution to be completely integrable. We give, under certain conditions, some relatio...

In this paper, we study a particular class of Hermitian manifolds which we call special c ' -hyperbolic Hermitian manifolds with c ' ∈ℝ, c ' ≠0. As main result, we prove that the universal covering space of a special c ' -hyperbolic Hermitian manifold is the product of a c- Sasakian manifold with a hyperbolic space of odd dimension and of constant...