Volume 21, Issue 4

In this article, we study the existence of positive solutions of a multi-point boundary value problem for some system of fractional differential equations. The fixed point theorem on cones will be applied to demonstrate the existence of solutions for this system. At the end, an example shows the application of the main results.

In this paper, totally free 2-quadratic modules are defined. It is shown that the category of totally free 2-quadratic complexes is a cofibration category in the sense of Baues.

Solutions are constructed for integro-differential equations related to problems of contact interaction of an elastic thin semi-infinite inclusion with the plane, when the plane material possesses the creep property, whereas the elastic and geometric parameters of the inclusion are measured along its length according to the power law.

Recently, the concept of weighted generator sequence has been introduced by Çanak and Totur [Comput. Math. Appl. 62 (2011), no. 6, 2609–2615]. They proved that certain conditions in terms of weighted generator sequences are Tauberian conditions for the weighted mean method. In this paper, we present the necessary and sufficient Tauberian conditions based on a weighted generator sequence under which statistical convergence follows from statistical summability by weighted means.

In the present paper, we establish some new Opial-type integral inequalities in two variables. The results in special cases yield some of the interrelated results on Godunova–Levin's and Mitrinović–Pečarić's inequalities. These results provide new estimates on inequalities of this type.

This paper investigates the underlying structure of the n -th derivative of e s · x 1/2 with respect to x . For n ∈ ℤ + , ( d n / d x n ) e s · x 1/2 can be expressed in terms of spherical modified Bessel functions of second kind in the complex plane. The representation holds for n ∈ ℤ - , where it represents the particular n -th antiderivative of e s · x 1/2 with all n constants of integration equal to zero. Our results introduce new connections among mathematical applications and provide some Bessel properties.

We consider a mathematical frictionless contact problem between two electro-elastic bodies. The contact is modelled with normal compliance and adhesion. We provide a variational formulation for the problem and prove the existence of a unique weak solution. The proofs are based on arguments of time-dependent variational inequalities, the Cauchy–Lipschitz Theorem and the Banach Fixed-Point Theorem. Then, a discrete scheme is introduced based on the finite element method to approximate the spatial variable. Furthermore, we provide optimal a priori error estimates for the displacements, the electric potential and the bonding at the contact interface.

New function spaces Lp(·),θ$L^{ p(\,\cdot \,), \theta }$, ℒp(·),θ${\mathcal {L}}^{ p(\,\cdot \,), \theta }$ unifying grand Lebesgue spaces and variable exponent Lebesgue spaces are introduced. The boundedness of maximal and Calderón–Zygmund operators in these spaces defined on spaces of homogeneous type are derived. The Sobolev type theorem for fractional integrals is also established in the class of functions which is narrower than the space Lp(·),θ$L^{ p(\,\cdot \,),\theta }$.

In this paper we prove the stability result for the functional equation (1/ L )∑ λ∈K F ( x + λ y ) = G ( x ) + H ( y ), x , y ∈ S , for functions F , G , H : S → X , where ( S ,+) is an abelian semigroup, K is a finite subgroup of the automorphism group of S , L := | K |, ( X ,∥·∥) is the Banach space over a field 𝕂 ∈ {ℝ,ℂ}.

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay term in the feedback. The heat conduction is given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem. Furthermore, an exponential stability result is shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semigroup method and the energy method.

In this paper, we establish several new inequalities for s -convex mappings that are connected with the Riemann–Liouville fractional integrals. Our results have some relationships with an Ostrowski type integral inequality in the literature.

In this paper we introduce a new class of generalized Hermite–Legendre polynomials of 2-variables and consequently a new class of Tricomi, Bessel and Hermite polynomials and their generalizations starting from suitable generating functions. The theory of Bessel, Legendre, Hermite and of the associated generating functions and their generalizations is reformulated within the framework of a series rearrangement formalism by using different analytical means on their respective generating functions.

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Fejér means in terms of the modulus of continuity on the Hardy spaces H p when 0 < p ≤ 1/2.