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In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of ϵ-approximate solutions.

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

The purpose of this research is to investigate how to introduce a financing scheme to tackle the manufacturer's capital constraint problem, discuss the effects of data-driven marketing (DDM) quality, cross-channel-return (CCR) rate and financing interest rate on the members' pricing and delivery-lead-time decisions and optimal performances, and analyzes `how to achieve the coordination within a dual-channel supply chain (DSC) by contract coordination.

This work establishes a DSC model with DDM, and the offline retailer can provide internal financing to the capital-constrained online manufacturer. The demand under the price is determined based on DDM quality, customer channel preference and delivery lead time. Then, combined with the Stackelberg game, the optimal pricing and delivery-lead-time decisions are discussed under the inconsistent and consistent pricing strategies with decentralized and centralized systems. Furthermore, it designs a manufacturer-revenue sharing contract to coordinate the members under the two pricing strategies.

(1) The increase of DDM quality will reduce the delivery-lead-time under the inconsistent or consistent pricing strategy and will push the selling prices; (2) The growth of the CCR rate will raise selling prices and extend the delivery-lead-time under the decentralized decision; (3) Under price competition, the offline selling price is higher than the online selling price when customers prefer the offline channel and vice versa; (4) The retailer and the manufacturer can achieve a win-win situation through a manufacturer-revenue sharing contract.

This paper contributes to the studies related to DSC by investigating pricing and delivery-lead-time decisions based on DDM, CCR, internal financing and supply chain contract and proposes some managerial implications.

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

The present article deals with the initiation and study of a uniformity like notion, captioned μ-uniformity, in the context of a generalized topological space.

The existence of uniformity for a completely regular topological space is well-known, and the interrelation of this structure with a proximity is also well-studied. Using this idea, a structure on generalized topological space has been developed, to establish the same type of compatibility in the corresponding frameworks.

It is proved, among other things, that a μ-uniformity on a non-empty set X always induces a generalized topology on X, which is μ-completely regular too. In the last theorem of the paper, the authors develop a relation between μ-proximity and μ-uniformity by showing that every μ-uniformity generates a μ-proximity, both giving the same generalized topology on the underlying set.

It is an original work influenced by the previous works that have been done on generalized topological spaces. A kind of generalization has been done in this article, that has produced an intermediate structure to the already known generalized topological spaces.

The paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.

The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

In this paper, we study the different kinds of the primeness on the class of near-rings and we give new characterizations for them. For that purpose, we introduce new concepts called set-divisors, ideal-divisors, etc. and we give equivalent statements for 3-primeness which make 3-primeness looks like the forms of the other kinds of primeness. Also, we introduce a new different kind of primeness in near-rings called K-primeness which lies between 3-primeness and e-primeness. After that, we study different kinds of prime ideals in near-rings and find a connection between them and new concepts called set-attractors, ideal-attractors, etc. to make new characterizations for them. Also, we introduce a new different kind of prime ideals in near-rings called K-prime ideals.

Hamming distance of a two bit strings u and v of length n is defined to be the number of positions of u and v with different digit. If G is a simple graph on n vertices and m edges and B is an edge–vertex incidence matrix of G, then every edge e of G can be labeled using a binary digit string of length n from the row of B which corresponds to the edge e. We discuss Hamming distance of two different edges of the graph G. Then, we present formulae for the sum of all Hamming distances between two different edges of G, particularly when G is a path, a cycle, and a wheel, and some composite graphs.

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

A flexible model which is based on a Triangular intuitionistic flexibility ranking and aggregating (TIFRA) operator is proposed for failure detection and reliability management in a Wind Turbine system. The model which is employed when there are limited research data and valid source of information, uses expert-based knowledge/opinion for failure detection and reliability management. The results from the study concludes that, the most important area affected by failure with respect to the failure criteria used, includes; oil level sensor tilt sensors for tower installation and accelerometers for tower sway (A₂), Pressure sensor for blade monitoring (A₃), and the Pitch actuator (A₄). The main advantage of the proposed method is that it provides advanced information about faults that identifies the intensity of the system behavior also; the method provides a more complete view of the reliability management and root cause of failure in the Wind Turbine (WT) system using the flexibility parameter in the model.