# Showing papers in "Mediterranean Journal of Mathematics in 2018"

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TL;DR: In this paper, the authors established the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer's fixed point theorem and Banach contraction principle, and established the equivalent mixed-type integral for nonlocal condition.

Abstract: The aim of this paper is to establish the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer’s fixed point theorem and Banach contraction principle. Next, we establish the equivalent mixed-type integral for nonlocal condition. Further we prove the Ulam stability results. The Gronwall’s lemma for singular kernels plays an important role to prove our results. We verify our results by providing examples.

86 citations

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TL;DR: A new family of effectively nine stages, ninth-order hybrid explicit Numerov-type methods is presented for the solution of some special second order Initial Value Problem, from which an optimal constant coefficients method is derived along with a similar kind of method with reduced phase errors.

Abstract: A new family of effectively nine stages, ninth-order hybrid explicit Numerov-type methods is presented for the solution of some special second order Initial Value Problem. After dealing with a reduced set of order conditions, we derive an optimal constant coefficients method along with a similar kind of method with reduced phase errors. We proceed with numerical tests using quadruple precision arithmetic on some well-known problems from the relevant literature. Finally, in the appendices, we list Mathematica packages implementing the corresponding algorithms.

56 citations

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TL;DR: In this article, an effectively four-stage, sixth-order, hybrid explicit Numerov-type method is presented for the solution of the special second-order initial value problem.

Abstract: An effectively four-stage, sixth-order, hybrid explicit Numerov-type method is presented for the solution of the special second-order initial value problem. The new method uses variable step, is trigonometric fitted and the phase-lag is nullified along with its first and second derivative. Extensive numerical tests illustrate the superiority of our proposal over similar methods found in the relevant literature.

52 citations

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TL;DR: In this article, the authors obtained new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform).

Abstract: We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann–Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.

50 citations

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TL;DR: In this article, the study of Yamabe and quasi-Yamabe solitons on Euclidean submanifolds whose soliton fields are the tangential components of their position vector fields was initiated.

Abstract: In this paper, we initiate the study of Yamabe and quasi-Yamabe solitons on Euclidean submanifolds whose soliton fields are the tangential components of their position vector fields. Several fundamental results of such solitons were proved. In particular, we classify such Yamabe and quasi-Yamabe solitons on Euclidean hypersurfaces.

49 citations

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TL;DR: In this article, a kind of Euler polynomials and its basic properties are studied in detail, and two specific exponential generating functions are defined and applied to computing new series of Taylor types that contain the associated Euler numbers.

Abstract: By defining two specific exponential generating functions, we introduce a kind of Euler polynomials and study its basic properties in detail. As an application of the introduced polynomials, we use them in computing some new series of Taylor type that contain the associated Euler numbers $$E_n(0)$$
where $$E_n(x)$$
is the Euler polynomial.

37 citations

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TL;DR: In this paper, the authors analyse the relationship between different extremal notions in Lipschitz free spaces (strongly exposed, exposed, preserved extreme and extreme points) and prove that every preserved extreme point of the unit ball is also a denting point.

Abstract: We analyse the relationship between different extremal notions in Lipschitz free spaces (strongly exposed, exposed, preserved extreme and extreme points). We prove in particular that every preserved extreme point of the unit ball is also a denting point. We also show in some particular cases that every extreme point is a molecule, and that a molecule is extreme whenever the two points, say x and y, which define it satisfy that the metric segment [x, y] only contains x and y. The most notable among them is the case when the free space admits an isometric predual with some additional properties. As an application, we get some new consequences about norm attainment in spaces of vector-valued Lipschitz functions.

36 citations

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TL;DR: In this article, the authors considered the fractional r-Laplacian problem with critical Sobolev-Hardy exponents and showed that infinitely many solutions tend to be zero.

Abstract: We consider the following fractional $$ p \& q$$
Laplacian problem with critical Sobolev–Hardy exponents $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}_{p} u + (-\Delta )^{s}_{q} u = \frac{|u|^{p^{*}_{s}(\alpha )-2}u}{|x|^{\alpha }}+ \lambda f(x, u) &{} \text{ in } \Omega \\ u=0 &{} \text{ in } \mathbb {R}^{N}{\setminus } \Omega , \end{array} \right. \end{aligned}$$
where $$0

30 citations

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TL;DR: In this article, the authors introduce a new class of operators in vector lattices, called orthogonally additive laterally-to-order bounded operators, which are not order bounded.

Abstract: In this paper, we introduce a new class of operators in vector lattices. We say that orthogonally additive operator T from vector lattice E to vector lattice F is laterally-to-order bounded if for any element x of E an operator T maps the set $$\mathcal {F}_{x}$$
of all fragments of x onto an order bounded subset of F. We get a lattice calculus of orthogonally additive laterally-to-order bounded operators defined on a vector lattice and taking values in a Dedekind complete vector lattice. It turns out that these operators, in general, are not order bounded. We investigate the band of laterally continuous orthogonally additive operators and obtain formulas for the order projection onto this band. We consider the procedure of the extension of an orthogonally additive operator from a lateral ideal to the whole space. Finally we obtain conditions on the integral representability for a laterally-to-order bounded orthogonally additive operator.

29 citations

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TL;DR: In this article, a type of second-order neutral differential equations with variable coefficient and delay was discussed, and sufficient conditions for the existence of periodic solutions were established. But the conditions for periodic solutions are not defined.

Abstract: In this article, we discuss a type of second-order neutral differential equations with variable coefficient and delay: $$\begin{aligned} (x(t)-c(t)x(t-\tau (t)))''+a(t)x(t)=f(t,x(t-\delta (t))), \end{aligned}$$
where $$c(t)\in C({\mathbb {R}},{\mathbb {R}})$$
and $$|c(t)|
e 1$$
. By employing Krasnoselskii’s fixed-point theorem and properties of the neutral operator $$(Ax)(t):=x(t)-c(t)x(t-\tau (t))$$
, some sufficient conditions for the existence of periodic solutions are established.

28 citations

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TL;DR: In this article, an existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference systems with a time delay was investigated. But the uniqueness theorem was not applied to the solution of the nonlinear NDFS with a delay.

Abstract: In this paper, we investigate an existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay. More precisely, observing $$
u (t-k)^{\overline{
u -1}}\le {t^{\bar{
u }}}$$
, we get the evaluation of $$
abla _{a+k}^{-
u } ||z(t-k)||$$
, which allows us to apply the generalized Gronwall’s inequality for the solutions of nonlinear nabla fractional difference system. The theorems we establish fill the gaps in some existing papers.

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TL;DR: In this paper, the authors investigated the entire and meromorphic solutions of the Fermat-type functional equations such as partial differential-difference equation and partial difference equation by making use of Nevanlinna theory for meromorphic functions in several complex variables.

Abstract: The functional equation $$f^{m}+g^{m}=1$$ can be regarded as the Fermat-type equations over function fields. In this paper, we investigate the entire and meromorphic solutions of the Fermat-type functional equations such as partial differential-difference equation $$\left( \frac{\partial f(z_{1}, z_{2})}{\partial z_{1}}\right) ^{n}+f^{m}(z_{1}+c_{1}, z_{2}+c_{2})=1$$ in $$\mathbb {C}^{2}$$ and partial difference equation $$f^{m}(z_{1}, \ldots , z_{n})+f^{m}(z_{1}+c_{1}, \ldots , z_{n}+c_{n})=1$$ in $$\mathbb {C}^{n}$$ by making use of Nevanlinna theory for meromorphic functions in several complex variables.

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TL;DR: In this article, a sharp inequality for the squared norm of the second fundamental form of bi-warped product submanifolds of Kenmotsu manifolds has been established.

Abstract: In this paper, we establish a sharp inequality for the squared norm of the second fundamental form of bi-warped product submanifolds of Kenmotsu manifolds. The equality case is also considered. We also provide a non-trivial example and some applications of derived inequality.

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TL;DR: In this article, a high-order B-spline collocation method on a uniform mesh is presented for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions.

Abstract: In this paper, a high-order B-spline collocation method on a uniform mesh is presented for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions: $$\begin{aligned} (p(x)y')'= & {} p(x)f(x,y), \quad 0

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TL;DR: In this article, a new numerical approach has been proposed for solving a class of delay time-fractional partial differential equations, where the approximate solutions of these equations are considered as linear combinations of Muntz-Legendre polynomials with unknown coefficients.

Abstract: In this article, a new numerical approach has been proposed for solving a class of delay time-fractional partial differential equations. The approximate solutions of these equations are considered as linear combinations of Muntz–Legendre polynomials with unknown coefficients. Operational matrix of fractional differentiation is provided to accelerate computations of the proposed method. Using Pade approximation and two-sided Laplace transformations, the mentioned delay fractional partial differential equations will be transformed to a sequence of fractional partial differential equations without delay. The localization process is based on the space-time collocation in some appropriate points to reduce the fractional partial differential equations into the associated system of algebraic equations which can be solved by some robust iterative solvers. Some numerical examples are also given to confirm the accuracy of the presented numerical scheme. Our results approved decisive preference of the Muntz–Legendre polynomials with respect to the Legendre polynomials.

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TL;DR: In this article, the structure of Jordan centralizers and generalized derivations on 2-torsion-free triangular rings through commutative zero products are given, and some corollaries concerning (Jordan) centralizers are obtained.

Abstract: In this article, the structure of Jordan centralizers and Jordan generalized derivations on 2-torsion-free triangular rings through commutative zero products are given. By applying this results, we obtain some corollaries concerning (Jordan) centralizers and (Jordan) derivations on triangular rings.

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TL;DR: In this article, the existence and uniqueness of nonnegative solutions of an initial value problem for Langevin equations involving two fractional orders were studied. But the main tools are fixed point theorems in partially ordered metric spaces.

Abstract: In this paper, we study the existence and uniqueness of nonnegative solutions of an initial value problem for Langevin equations involving two fractional orders: $$\begin{aligned} \left\{ \begin{array}{lll}^c_0\!D^\beta _t({}^c_0\!D^\alpha _t-\gamma )x(t)=f(t,x(t)),&{}\quad \ 0< t<1,\\ x^{(k)}(0)=\mu _k,&{}\quad \ 0\le k

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TL;DR: In this paper, the authors studied non-finitely generated submodules with chain condition and showed that if an R-module M satisfies the ascending chain condition on NGs, then every submodule of M is countably generated.

Abstract: In this article, we study modules with chain condition on non-finitely generated submodules. We show that if an R-module M satisfies the ascending chain condition on non-finitely generated submodules, then M has Noetherian dimension and its Noetherian dimension is less than or equal to one. In particular, we observe that if an R-module M satisfies the ascending chain condition on non-finitely generated submodules, then every submodule of M is countably generated. We investigate that if an R-module M satisfies the descending chain condition on non-finitely generated submodules, then M has Krull dimension and its Krull dimension may be any ordinal number $$\alpha $$
. In particular, if a perfect R-module M satisfies the descending chain condition on non-finitely generated submodules, then it is Artinian.

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TL;DR: In this article, the authors established the local well-posedness of strong solutions to the Cauchy problem of the incompressible viscous resistive Hall-MHD equations and proved that the local solution is global when the initial data is small enough.

Abstract: In this paper, we first establish the local well-posedness of strong solutions to the Cauchy problem of the incompressible viscous resistive Hall-MHD equations in $$H^s(\mathbb {R}^3)$$
$$(\frac{3}{2}< s\le \frac{5}{2})$$
, and then we prove that the local solution is global when the initial data is small enough.

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TL;DR: In this article, a class of degenerate p-fractional Kirchhoff equations with critical Hardy-Sobolev nonlinearities was studied and the existence of infinitely many solutions which tend to zero under a suitable value of $$\lambda $$

Abstract: In this paper, we study a class of degenerate p-fractional Kirchhoff equations with critical Hardy–Sobolev nonlinearities. By means of the Kajikiya’s new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero under a suitable value of $$\lambda $$
. The main feature and difficulty of our equations is the fact that the Kirchhoff term M could be zero at zero, that is the equation is degenerate. To our best knowledge, our results are new even in the Laplacian and p-Laplacian cases.

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TL;DR: In this article, the existence and uniqueness of positive solutions of a kind of multi-point boundary value problems for nonlinear fractional differential equations with p-Laplacian operator using the Banach contraction mapping principle were investigated.

Abstract: In this paper, we investigate the existence and uniqueness of positive solutions of a kind of multi-point boundary value problems for nonlinear fractional differential equations with p-Laplacian operator using the Banach contraction mapping principle. Furthermore, some examples are given to illustrate our results.

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TL;DR: Anguiano and Suarez-Grau as discussed by the authors considered a 3D incompressible Navier-Stokes system where the external force takes values in the space, and the porous medium considered has one commonly used distribution of cylinders: hexagonal distribution.

Abstract: We consider a Newtonian flow in a thin porous medium $$\Omega _{\varepsilon }$$
of thickness $$\varepsilon $$
which is perforated by periodically distributed solid cylinders of size $$a_\varepsilon $$
. Generalizing (Anguiano and Suarez-Grau, ZAMP J Appl Math Phys 68:45, 2017), the fluid is described by the 3D incompressible Navier–Stokes system where the external force takes values in the space $$H^{-1}$$
, and the porous medium considered has one of the most commonly used distribution of cylinders: hexagonal distribution. By an adaptation of the unfolding method, three different Darcy’s laws are rigorously derived from this model depending on the magnitude $$a_{\varepsilon }$$
with respect to $$\varepsilon $$
.

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TL;DR: In this paper, the existence and nonuniqueness of nontrivial solutions for a class of fractional Hamiltonian systems with concave-convex potentials via the variational methods were studied.

Abstract: In this paper, we study the existence and nonuniqueness of nontrivial solutions for a class of fractional Hamiltonian systems with concave–convex potentials via the variational methods. A new twisted condition is introduced, which yields a new compact embedding theorem. Some results are new even for second-order Hamiltonian systems.

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TL;DR: In this paper, the p(x)-Laplacian Robin eigenvalue problem was considered and the existence of a continuous family of eigenvalues in a neighborhood of the origin using variational methods was established.

Abstract: We consider the p(x)-Laplacian Robin eigenvalue problem $$\begin{aligned} \left\{ \begin{array}{ll} - \Delta _{p(x)}u = \lambda V(x) |u|^{q(x)-2}u, \quad x\in \Omega ,\\ |
abla u|^{p(x)-2}\frac{\partial u}{\partial
u }+\beta (x)|u|^{p(x)-2}u=0,\quad x\in \partial \Omega , \end{array}\right. \end{aligned}$$
where $$\Omega $$
is a bounded domain in $$\mathbb {R}^N$$
with smooth boundary $$\partial \Omega $$
, $$N\ge 2$$
, $$\frac{\partial u}{\partial
u }$$
is the outer normal derivative of u with respect to $$\partial \Omega $$
, $$p,q\in C_+(\overline{\Omega })$$
, $$1

0$$ , and $$\lambda >0$$ is a parameter. Under some suitable conditions on the functions q and V, we establish the existence of a continuous family of eigenvalues in a neighborhood of the origin using variational methods. The main results of this paper improve and generalize the previous ones introduced in Deng (J Math Anal Appl 360:548–560, 2009), Kefi (Zeitschrift fur Analysis und ihre Anwendungen (ZAA) 37:25–38, 2018).

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TL;DR: In this paper, the second-type almost geodesic mappings are obtained for the Weyl projective tensor and the Thomas projective parameter, which are generalizations of Weyl tensors.

Abstract: Invariants of second-type almost geodesic mappings are obtained in this paper. These invariants are generalizations of Thomas projective parameter and Weyl projective tensor.

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TL;DR: In this article, the Browder-type and Weyl-type theorems for operators of the form T+K+K on a Banach space X, where T is a compact operator and K is a non necessarily commuting operator on X, were studied.

Abstract: In this paper, we study Browder-type and Weyl-type theorems for operators $$T+K$$
defined on a Banach space X, where K is (a non necessarily commuting) compact operator on X. In the last part, the theory is exemplified in the case of isometries, analytic Toeplitz operators, semi-shift operators, and weighted right shifts.

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TL;DR: In this paper, necessary and sufficient conditions of the one-sided reverse order law are given in rings with involution for the core inverse, and mixed-type reverse order laws are also considered.

Abstract: In this paper, necessary and sufficient conditions of the one-sided reverse order law $$(ab)^{\tiny {\textcircled {\tiny \#}}}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$
, the two-sided reverse order law $$(ab)^{\tiny {\textcircled {\tiny \#}}}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$
and $$(ba)^{\tiny {\textcircled {\tiny \#}}}=a^{\tiny {\textcircled {\tiny \#}}}b^{\tiny {\textcircled {\tiny \#}}}$$
for the core inverse are given in rings with involution. In addition, the mixed-type reverse order laws, such as $$(ab)^{\#}=b^{\tiny {\textcircled {\tiny \#}}}(abb^{\tiny {\textcircled {\tiny \#}}})^{\tiny {\textcircled {\tiny \#}}}$$
, $$a^{\tiny {\textcircled {\tiny \#}}}=b(ab)^{\#}$$
and $$(ab)^{\#}=b^{\tiny {\textcircled {\tiny \#}}}a^{\tiny {\textcircled {\tiny \#}}}$$
, are also considered.

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TL;DR: In this paper, a variant of the Jensen-Mercer operator inequality is proved for a superquadratic function and positive linear operators on a Hilbert space using a theorem of Neumark.

Abstract: A variant of the Jensen–Mercer operator inequality is proved for a superquadratic function and positive linear operators on a Hilbert space using a theorem of Neumark. Moreover, function order preserving operator inequalities for superquadratic functions is established. As application, a Kantorovich-type order preserving operator inequality via the Ky Fan–Furuta constant is obtained.

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TL;DR: In this article, two numerical schemes for solving the Ito stochastic differential systems were proposed based on the Euler-Maruyama method, which are analyzed under the Lipschitz and linear growth conditions.

Abstract: In this paper, by composite previous-current-step idea, we propose two numerical schemes for solving the Ito stochastic differential systems. Our approaches, which are based on the Euler–Maruyama method, solve stochastic differential systems with strong sense. The mean-square convergence theory of these methods are analyzed under the Lipschitz and linear growth conditions. The accuracy and efficiency of the proposed numerical methods are examined by linear and nonlinear stochastic differential equations.

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TL;DR: In this article, a fixed point theorem for systems of nonlinear operator equations is established by means of topological degree theory and positively 1-homogeneous operator, where the components has a positively 1homogeneous majorant or minorant.

Abstract: A new fixed point theorem for systems of nonlinear operator equations is established by means of topological degree theory and positively 1-homogeneous operator, where the components has a positively 1-homogeneous majorant or minorant. As applications, the existence of positive solutions for $$(p_1, p_2)$$
-Laplacian system is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1-homogeneous operators.