Abstract: In this paper we consider a class of fractional nonlinear neutral stochastic evolution inclusions with nonlocal initial conditions in Hilbert space. Using fractional calculus, stochastic analysis theory, operator semigroups and Bohnenblust–Karlin’s fixed point theorem, a new set of sufficient conditions are formulated and proved for the existence of solutions and the approximate controllability of fractional nonlinear stochastic differential inclusions under the assumption that the associated linear part of the system is approximately controllable. An example is provided to illustrate the theory. PubDate: 2017-02-21

Abstract: The purpose of this paper is to introduce Picard–Krasnoselskii hybrid iterative process which is a hybrid of Picard and Krasnoselskii iterative processes. In case of contractive nonlinear operators, our iterative scheme converges faster than all of Picard, Mann, Krasnoselskii and Ishikawa iterative processes in the sense of Berinde (Iterative approximation of fixed points, 2002). We support our analytic proofs with a numerical example. Using this iterative process, we also find the solution of delay differential equation. PubDate: 2017-02-16

Abstract: This paper presents an analysis of a Markovian feedback queueing system with reneging and retention of reneged customers, multiple working vacations and Bernoulli schedule vacation interruption, where customers’ impatience is due to the servers’ vacation. The reneging times are assumed to be exponentially distributed. After the completion of service, each customer may reenter the system as a feedback customer for receiving another regular service with some probability or leave the system. A reneged customer can be retained in many cases by employing certain convincing mechanisms to stay in queue for completion of service. Thus, a reneged customer can be retained in the queueing system with some probability or he may leave the queue without receiving service. We establish the stationary analysis of the system. The probability generating functions of the stationary state probabilities is obtained, we deduce the explicit expressions of the system sizes when the server is in a normal service period and in a Bernoulli schedule vacation interruption, respectively. Various performance measures of the system are derived. Finally, we present some numerical examples to demonstrate how the various parameters of the model influence the behavior of the system. PubDate: 2017-01-20

Abstract: We develop the Benkhettou–Hassani–Torres fractional (noninteger order) calculus on timescales by proving two chain rules for the \(\alpha \) -fractional derivative and five inequalities for the \(\alpha \) -fractional integral. The results coincide with well-known classical results when the operators are of (integer) order \(\alpha = 1\) and the timescale coincides with the set of real numbers. PubDate: 2016-12-27

Abstract: In this paper, we introduce some new concepts to the field of probability theory: \(\left( k,s\right) \) -Riemann–Liouville fractional expectation and variance functions. Some generalized integral inequalities are established for \(\left( k,s\right) \) -Riemann–Liouville expectation and variance functions. PubDate: 2016-12-26

Abstract: This paper is a survey on bubbling phenomena occurring in some geometric problems. We present here a few problems from conformal geometry, gauge theory and contact geometry and we give the main ideas of the proofs and important results. We focus in particular on the Yamabe type problems and the Weinstein conjecture, where A. Bahri made a huge contribution by introducing new methods in variational theory. PubDate: 2016-12-26

Abstract: We study the nonexistence of nontrivial solutions for the nonlinear elliptic system $$\begin{aligned} \left\{ \begin{array}{lll} (-\Delta _x)^{\alpha /2}u+ x ^{2\delta } (-\Delta _y)^{\beta /2}u+ x ^{2\eta } y ^{2\theta } (-\Delta _z)^{\gamma /2}u&{}=&{} v^p,\\ \\ (-\Delta _x)^{\mu /2}v+ x ^{2\delta } (-\Delta _y)^{\nu /2}v+ x ^{2\eta } y ^{2\theta } (-\Delta _z)^{\sigma /2}v&{}=&{} u^q, \\ \end{array} \right. \end{aligned}$$ where \((x,y,z)\in \mathbb {R}^{N_1}\times \mathbb {R}^{N_2}\times \mathbb {R}^{N_3}\) , \(0<\alpha ,\beta ,\gamma ,\mu , \nu , \sigma \le 2\) , \(\delta , \eta ,\theta \ge 0\) , and \(p,q>1\) . Here, \((-\Delta _x)^{\alpha /2}\) , \(0<\alpha <2\) , is the fractional Laplacian operator of order \(\alpha /2\) with respect to the variable \(x\in \mathbb {R}^{N_1}\) , \((-\Delta _y)^{\beta /2}\) , \(0<\beta <2\) , is the fractional Laplacian operator of order \(\beta /2\) with respect to the variable \(y\in \mathbb {R}^{N_2}\) , and \((-\Delta _z)^{\gamma /2}\) , \(0<\gamma <2\) , is the fractional Laplacian operator of order \(\gamma /2\) with respect to the variable \(z\in \mathbb {R}^{N_3}\) . Using a weak formulation approach, sufficient conditions are provided in terms of space dimension and system parameters. PubDate: 2016-12-19

Abstract: In this paper, we establish sufficient conditions for the existence of local solutions for a class of Cauchy type problems with arbitrary fractional order. The results are established by the application of the contraction mapping principle and Schaefer’s fixed point theorem. An example is provided to illustrate the applicability of the results. PubDate: 2016-12-01

Abstract: Let a simply-connected homogeneous space \({X}\) satisfy the condition of \({{\rm dim} \pi_{\rm even}(X)\otimes {\mathbb{Q}}=2}\) and \({{\rm dim} \pi_{\rm odd}(X)\otimes {\mathbb{Q}}=3}\) (then, we say it is of (2, 3) type), which is the smallest rank in non-formal pure spaces. Then, we compute the Sullivan minimal model of the Dold–Lashof classifying space \({{\rm Baut}_1 X}\) according to Nishinobu and Yamaguchi (Topol Appl 196:290–307, 2015) and observe whether or not its rational cohomology is a polynomial algebra, which is a necessary condition for the Serre spectral sequence of any fibration over a sphere with fibre \({X}\) to degenerate at term \({E_2}\) . PubDate: 2016-10-31

Abstract: In this paper, we consider the problem of prescribing scalar curvature under minimal boundary conditions on the standard four-dimensional half sphere. We describe the lack of compactness of the associated variational problem and we give new existence and multiplicity results. PubDate: 2016-10-12

Abstract: Let M be a module over a commutative ring R. The annihilating-submodule graph of M, denoted by AG(M), is a simple graph in which a non-zero submodule N of M is a vertex if and only if there exists a non-zero proper submodule K of M such that N K = (0), where N K, the product of N and K, is denoted by (N : M)(K : M)M and two distinct vertices N and K are adjacent if and only if N K = (0). This graph is a submodule version of the annihilating-ideal graph. We prove that if AG(M) is a tree, then either AG(M) is a star graph or a path of order 4 and in the latter case \({M\cong F \times S}\) , where F is a simple module and S is a module with a unique non-trivial submodule. Moreover, we prove that if M is a cyclic module with at least three minimal prime submodules, then gr(AG(M)) = 3 and for every cyclic module M, \({cl({\rm AG}(M)) \geq {\rm Min}(M) }\) . PubDate: 2016-09-20

Abstract: In this paper, we introduce a cyclic subgradient extragradient algorithm and its modified form for finding a solution of a system of equilibrium problems for a class of pseudomonotone and Lipschitz-type continuous bifunctions. The main idea of these algorithms originates from several previously known results for variational inequalities. The proposed algorithms are extensions of the subgradient extragradient method for variational inequalities to equilibrium problems and the hybrid (outer approximation) method. The paper can help in the design and analysis of practical algorithms and gives us a generalization of the most convex feasibility problems. PubDate: 2016-08-03

Abstract: Let A be a \({\mathbb{k}}\) -algebra and \({A[t; \alpha,\delta]}\) its Ore extension. We give a pair of adjoint functors between the module category over ker \(\delta\) and the module category over \({A[t; \alpha,\delta]}\) . For a kind of special Ore extensions, this pair describes an equivalence between the module category over ker \({\delta}\) and an appropriate subcategory of the module category over \({A[t; \alpha,\delta]}\) . Applied to the case of Weyl algebras, this is exactly a Kashiwara’s theorem about D-modules. PubDate: 2016-08-02

Abstract: A class of periodic boundary value problems for higher order fractional differential equations with impulse effects is considered. We first convert the problem to an equivalent integral equation. Then, using a fixed-point theorem in Banach space, we establish existence results of solutions for this kind of boundary value problem for impulsive singular higher order fractional differential equations. Two examples are presented to illustrate the efficiency of the results obtained. PubDate: 2016-08-02

Abstract: We prove some new theta-function identities for two continued fractions of Ramanujan which are analogous to those of Ramanujan–Göllnitz–Gordon continued fraction. Then these identities are used to prove new general theorems for the explicit evaluations of the continued fractions. PubDate: 2016-08-02

Abstract: In this paper, we introduce (p, q)-Bernstein Durrmeyer operators. We define (p, q)-beta integral and use it to obtain the moments of the operators. We obtain uniform convergence of the operators by using Korovkin’s theorem. We estimate direct results of the operators by means of modulus of continuity and Peetre K-functional. Finally, we find Voronovskaya-type theorem for the operators. PubDate: 2016-08-02

Abstract: We investigate problems of estimating the deviation of functions from their de la Vallée-Poussin sums in weighted Orlicz spaces L M (T, ω) in terms of the best approximation \({E_{n}(f)_{M, \, \omega }}\) . PubDate: 2016-06-27

Abstract: In this article, a numerical technique is developed for solving delay differential equations. The proposed method combines the method of steps with the radial basis function networks. A delay differential equation is transformed to an ordinary differential equation and then the radial basis function collocationmethod is implemented to find the solution of the ordinary differential equation. The procedure for implementation of the radial basis function collocation method and the proposed method for delay differential equation is presented in detail. Numerical experiments are carried out on a number of examples to show the advantages of the proposed technique over the radial basis function collocation method. PubDate: 2016-05-07

Abstract: In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called quasi generalized Cauchy–Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficient conditions for some distributions to be integrable. PubDate: 2016-04-06

Abstract: For a positive integer k ≥ 2, the kth-order slant weighted Toeplitz operator \({U_{k,\phi}^{\beta}}\) on \({L^{2}(\beta)}\) with \({\phi \in L^{\infty}(\beta)}\) is defined as \({U_{k,\phi}^{\beta}=W_{k}M_{\phi}^{\beta}}\) , where \({W_{k}e_{n}(z)=\frac{\beta_{m}}{\beta_{km}}e_m(z)}\) if \({n=km, m\in\mathbb{Z}}\) and \({W_{k}e_n(z)= 0}\) if n ≠ km. The paper derives relations among the symbols of two kth-order slant weighted Toeplitz operators so that their product is a kth-order slant weighted Toeplitz operator. We also discuss the compactness and the case for two kth-order slant weighted Toeplitz operators to commute essentially. PubDate: 2015-12-17