Musaad Sabih Aldhabani

This paper investigates the resilient leader–follower consensus problem for a class of memory-dependent fractional-order multi-agent systems (FOMASs) with mixed communication delays, uncertain nonlinear dynamics, norm-bounded parametric uncertainties, and intermittent Denial-of-Service (DoS) attacks. The goal is to ensure that the follower agents follow the leader’s path even in the event of weak links, network changes, and lost communications. An adaptive radial basis function neural network (RBFNN) is used as an online approximator to cover the unmodeled nonlinearity. The two complementary delay configurations studied are a discrete-delay protocol, which features a fixed delay on the state, communication channel, and control input; and a distributed-delay protocol, which carries a memory of past states on the control input but a cumulative memory of past states on the DoS-induced input disturbance. In both scenarios, adequate linear matrix inequality (LMI) conditions are obtained in a Lyapunov–Razumikhin stability setting ensuring leader-following consensus, plus a less demanding version of the LMI conditions expressed in terms of eigenvalues, tailored for Kronecker-structured, large-scale networks. A condition of an average dwell-time is used to establish an average condition on the frequency of DoS attack to certify the robustness against intermittent communication disruption. The effectiveness of the proposed RBFNN-based resilient consensus framework is demonstrated by numerical simulation on a network of six followers, with the discrete-delay and distributed-delay configurations each validated separately; the scalability of the eigenvalue-based feasibility-verification test relative to the full LMI synthesis is examined with growing network size, and an ablation study is carried out to isolate the effect of the RBFNN compensation and the dwell-time-consistent gain design. The fully combined discrete-and-distributed-delay case is formulated but not numerically simulated in this work.

This research analyzes transient transport phenomena regarding thermal and concentration in a Casson fluid-based hybrid nanofluid system containing copper (Cu) and aluminum oxide (Al ₂ O ₃ ) nanoparticles. Unlike existing works, this study introduces a novel framework that concurrently incorporates four interconnected physical mechanisms, chemical reaction kinetics, applied magnetic field effects (MHD), radiative heat transfer, and interfacial slip dynamics over an unsteady stretching elastic surface. This simultaneous treatment of coupled phenomena, which has not been previously explored in combination, provides a more holistic and physically realistic model. The results offer valuable insights for applications requiring precise thermal and mass transfer management, such as advanced thermal management systems, intelligent polymer manufacturing, energy conversion technologies, and high-performance nanofluidic lubricants. Through employing similarity analysis, the original governing equations are transformed into a system of highly nonlinear ordinary differential equations, which are solved computationally via shooting technique to evaluate how key dimensionless parameters impact hydrodynamic and transport characteristics. The computational findings reveal a substantial degree of control over the transfer of momentum, heat, and mass, offering essential guidance for optimizing various industrial-processes. The main findings of the study demonstrates that both thermal and concentration slip effects suppress transport rates, with the Nusselt and Sherwood numbers decreasing monotonically as their respective slip parameters enhance. Also, the thermal radiation intensifies the temperature distribution by thickening the thermal boundary layer, whereas thermal slip diminishes wall heat flux, thereby reducing the local Nusselt number and highlighting their opposing influences. Computational and analytical solutions show excellent agreement with established benchmark cases through comparison with previous studies, exhibiting no noticeable deviation in the obtained results and thereby confirming the reliability of the model.

In this study, we presented the conformable Laplace transform iterative method to find the approximate solution of the systems of nonlinear temporal-fractional differential equations in the sense of the conformable derivative. The advantage of the suggested approach was to compute the solution without discretization and restrictive assumptions. Three distinct examples were provided to show the applicability and efficacy of the proposed approach. To examine the exact and approximate solutions, we utilized the 2D and 3D graphics. Furthermore, the outcomes produced in this study were consistent with the exact solutions; hence, this strategy efficiently and effectively determined exact and approximate solutions to nonlinear temporal-fractional differential equations.

In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CNHEs). This system models the transmission of optical solitons and coupled wave packets in nonlinear optical fibers and describes transverse effects in nonlinear fiber optics. Initially, a complex transformation is used to convert the model into a single Nonlinear Ordinary Differential Equation (NODE), from which hyperbolic, exponential, rational, trigonometric, and rational hyperbolic solutions are produced. In order to better understand the physical dynamics, we offer several 3D, contour, and 2D illustrations for the independent selections of physical parameter values. These illustrations highlight the graphic behaviour of some optical solitons and demonstrate that, under certain constraint conditions, acquired optical solitons lose their stability when they approach an axis and display periodic-axial perturbations, which lead to the generation of optical fractals. As a framework, the generated optical solitons have several useful applications in the field of telecommunications. Furthermore, our suggested RMESEM demonstrates its use by broadening the spectrum of optical soliton solutions, offering important insights into the dynamics of the CNHEs, and suggesting possible applications in the management of nonlinear models.

The objective of the paper is to present some fixed point results verifying a relational contraction utilizing certain shifting distance functions and via a generalized class of transitive relations. Our outcomes sharpen, extend, modify, and enrich many well‐known results. To demonstrate the utility of our results, several examples are provided. We employed our results finding out a unique solution of second‐order ordinary differential equations prescribed with specific boundary conditions.