Prescribed-time leader-following scaled consensus for nonlinear multiagent systems

In this paper, the leader-following (L-F) scaled consensus (SC) for first-order multiagent systems (MASs) is considered within a prescribed time (PT). First, a distributed control protocol is proposed by incorporating a time-varying gain function and scaled factors. This protocol is designed to drive the states of the leader and followers to a predefined scaled relationship within the PT. It is worth noting that, by appropriately selecting the scaled factor, the protocol can also achieve complete consensus, bipartite consensus, or cluster consensus among the agents. To further enhance the control performance and reduce communication frequency, an improved control protocol is proposed by incorporating an event-triggered mechanism in which the event-triggering function is constructed using time-varying variables. Moreover, based on the PT stability theory, sufficient conditions are derived to ensure that SC is achieved within the PT. Finally, the effectiveness of the proposed control protocol is verified through two numerical simulation examples

Existence and approximate controllability results for time-fractional stochastic Navier–Stokes equations

This paper deals with time-fractional stochastic Navier–Stokes equations, which are characterized by the coexistence of stochastic noise and a fractional power of the Laplacian. We establish sufficient conditions for the existence and approximate controllability of a unique mild solution to time-fractional stochastic Navier–Stokes equations. Using a fixed point technique, we first demonstrate the existence and uniqueness of a mild solution to the equation under consideration. We then establish approximate controllability results by using the concepts of fractional calculus, semigroup theory, functional analysis, and stochastic analysis

Exact solutions of stochastic generalized long–short wave resonance equations with cubic–quintic nonlinearity via the new sub-ODE method

We study a stochastic generalized long–short wave resonance system with cubic–quintic nonlinearities, perturbation terms, and multiplicative white noise in the Itô sense. Using a traveling-wave reduction combined with the newly proposed sub-ODE method, we construct explicit families of solitary-wave and elliptic-function solutions, including elevation, depression, and singular branches. The analysis reveals how stochastic effects shrink the existence domains of these solutions, while a Hamiltonian linearization provides Vakhitov–Kolokolov- and Grillakis–Shatah–Strauss-type stability criteria. The results enrich nonlinear wave theory and offer insights relevant to solitary-wave applications in fiber optics and related technologies

Joint ruin probability and risk contagion measure in a quota-share reinsurance risk model: An asymptotic approach

Consider a quota-share reinsurance risk model with constant premiums and stochastic returns in which an insurer purchases fixed-proportion quota-share reinsurance for its business line. Both the insurer and reinsurer may engage in risk-free investments, with their nonnegative general (not necessarily Lévy) log-price processes following an arbitrary dependence structure. Under the assumption that claim sizes are pairwise strongly quasiasymptotically independent and follow heavy-tailed distributions, this paper derives asymptotic formulas for two types of finite-time joint ruin probabilities and for a risk contagion measure from the insurer to the reinsurer. Furthermore, we conduct numerical studies to verify the accuracy of the derived asymptotic results, using the Monte Carlo method combined with an explicit order-3.0 weak scheme

Fundamental contractions in suprametric spaces: Analysis and applications

In this manuscript, we propose the notion of a strong extended s-suprametric space, a novel extension that outperforms both s-suprametric and extended suprametric spaces. It looks into the aspects of open and closed ball topologies within this structure. It also investigates the concepts of existence and uniqueness using basic contractions viz. Banach and Kannan contractions. Illustrative examples demonstrate how the strong extended s-suprametric space outperforms its extended equivalent. Our examples demonstrate the presence and distinctness of fixed points in this scenario. Furthermore, exploiting these newly launched results, the manuscript investigates the analysis of a boundary value problem, including diffusing chemical material constrained between parallel walls with related concentrations at the boundaries, taking into account supplied raw density and recognized absorbing coefficients. It also applies these insights to a nonlinear boundary value issue involving satellite web coupling in which a thin sheet joins two cylindrical spacecraft. This coupling causes nonlinearity, resulting in a separate boundary value issue influenced by radiation effects within the satellites

Existence and stability results for triple systems of fractional Sturm–Liouville–Langevin equations with cyclic boundary conditions

We investigate a triple system of fractional Sturm–Liouville–Langevin equations with cyclic antiperiodic boundary conditions. The fixed point theorem serves as a tool to establish the existence and uniqueness criteria for solutions. By applying the Banach contraction principle, we also obtain the Ulam–Hyers stability of the proposed system. Finally, examples are provided to illustrate main results

New strong convergence algorithms for general equilibrium and variational inequality problems and resolvent operators in Banach spaces

In this paper, we introduce two new algorithms for solving variational inequalities in Banach spaces. Our aim is finding a common element of the solution set of variational inequalities (for two inverse-strongly monotone operators) and an equilibrium problem and the set of fixed points of two relatively nonexpansive mappings and a family of resolvent operators. Then the strong convergence of the sequences generated by these algorithms to this element will be proved under suitable conditions. Finally, we provide a numerical example to illustrate our main results

Existence of positive solutions for tempered fractional differential equations with p-Laplacian operator

This paper investigates the existence of positive solutions for a specific category of p-Laplacian tempered fractional differential equations in which the nonlinear term f contains an integral operator θ. By employing fixed point theorems for sum operators in partially ordered Banach spaces, together with Krasnosel’skii fixed point theorem, the existence of positive solutions is established. Moreover, iterative sequences are constructed to approximate the unique positive solution of the problem. Finally, three examples are presented to illustrate the main results

Trajectory controllability of semilinear dynamic systems on time scales

This paper explores the trajectory controllability of semilinear dynamic systems defined over time scales, which is an important aspect in understanding and manipulating the behavior of such systems across discrete and continuous domains. We address the controllability of these systems under the assumption that the nonlinearities satisfy a Lipschitz-type condition. Our approach involves a detailed analysis of how these conditions impact the ability to steer the system’s state along a desired trajectory within a finite-time horizon. We establish sufficient conditions for trajectory controllability (T-controllability), providing a theoretical framework that extends classical results from differential and difference equations to the broader context of time-scale calculus. To illustrate the practical implications of our theoretical findings, we include several numerical examples that demonstrate the application of our results to specific semilinear dynamic systems, highlighting the versatility and effectiveness of our approach