Vol. 10, No. 1 (2026): Regular Issue

A study of analytical methods is conducted in order to attain an approximate solution for the Magnetohydrodynamic Williamson nanofluid border layer flow via heat and mass transmission with velocity, thermal slip effects and radiation in a porous medium. The governing PDEs are converted into ODEs by utilizing similarity transformation. The semi-analytical expressions for the corresponding velocity, concentration and temperature gradients in non-dimensional form are attained via the Modified Homotopy Analysis Methodology (MHAM). A very excellent fit can be achieved when the analytical findings are compared to the numerical response. Numerous implications of the physical components occurred in the issue are graphically demonstrated. The factor of local skin friction, the Sherwood number, and the Nusselt number are all determined and highlighted in the table. Furthermore, the results exhibit how quickly and effectively the approach converges.

Transformable autonomous aerial systems possess intricate dynamics as a result of inherent nonlinearities and control uncertainties, which are frequently worsened by unmeasured disturbances caused by structural reconfiguration, such as spinning body components. To tackle these issues, it is essential to have a software sensor (observer) that can estimate non-measurable states and a sophisticated method to reject disturbances. This work presents a novel cascade scheme controller that utilizes the Active Disturbance Rejection Control (ADRC) in the internal loop to address unforeseeable disturbances in nonlinear systems. At the same time, a separate loop employs a Backstepping controller based on the state variables Sliding Mode Observer (SMO), guaranteeing global stability for the entire system. We utilize these methodologies on a Reconfigurable Quadrotor, which serves as a Transformable Unmanned Aerial System. The Multiobjective Particle Swarm Optimization (MPSO) algorithm is utilized to achieve parameter synthesis for the entire system. Numerical simulations provide evidence of the system's exceptional performance in terms of robustness, energy optimization, and perturbation rejection.

In this article, the existence and optimal control of stochastic pantograph differential equation (SPDEs) involving the Hilfer fractional derivative (HFD) was investigated, in which a set of novel conditions were built to illustrate the existence via the Schaefer's fixed point theorem and uniqueness via the Banach fixed point theorem. The existence of optimal control pairs for the corresponding Lagrange control systems is then explored. Stochastic elements introduce randomness, capturing real-world unpredictability, while pantograph equations incorporate scaled past states. Moreover, an example was proposed to showcase the practical applicability of the theoretical results.

This article examines analytically, a fourth-order nonlinear generalized Ablowitz-Kaup-Newell-Segur water wave equation in fluid dynamics with a perturbation parameter. Utilizing the Lie theoretic approach, symmetries of the equation are secured and used to gain invariant solutions. We achieve various analytic solutions of the understudy equation through the techniques of Lie symmetry reductions together with direct integration which include elliptic, trigonometry and algebraic functions. We obtain periodic functions solutions of the equation. The power series solution of the equation is generated. Moreover, the Kudryashov technique is utilized whereby gaining hyperbolic function solution of the equation. We present graphical depictions of the results for more meaningful interpretation and discuss them. Conclusively, we secure conserved quantities of the aforementioned equation by employing both the general multiplier and Noether techniques. Moreover, the applications of various results achieved in the study in physical sciences are outlined which saw to the physical interpretations of the conserved vectors being explicated.

In this paper, impulsive periodic motions to the corresponding homoclinic orbits in an impulsively forced pendulum are obtained through the implicit mapping method. The periodic motions in the impulsive pendulum are determined from the specific mapping structure, and the corresponding stability and bifurcation analysis of the impulsive periodic motions are carried out. The bifurcation trees of the impulsive periodic motions to the impulsive homoclinic orbits are presented. The saddle-node and period-doubling bifurcations are obtained, and the impulsive homoclinic orbits are also achieved. The impulsive homoclinic orbits are relative to the corresponding impulsive periodic motions, which are called the homoclinic bifurcations of the impulsive periodic motions. The impulsive periodic motions and impulsive homoclinic orbits of the impulsive forced pendulum are illustrated for a better understanding of impulsive periodic motions in the impulsively forced pendulum. The infinite impulsive homoclinic orbits related all impulsive periodic motions can be found.