The role of sustainable development financing resources in achieving sustainable development goals is one of the most important topics talked about in the recent sustainable development conflict, especially in the developing countries. Using the Autoregressive Distributed Lag (ARDL) model over the period 2002–2018, this study attempts to better identify sustainable development financing resources and examine their role in simultaneously ensuring economic growth and achieving social and environmental objectives in 24 developing countries. We found that increases in official development assistance, public debt, and remittances impede economic growth and human development and increase environmental pollution. Thus, they inhibit sustainable development. However, our findings demonstrated that foreign direct investment and international trade, which enhance economic growth, do not have any effect on CO2 emissions, while foreign direct investment inflows boost human development and international trade seems detrimental to it. Our study also show the effectiveness of CREDIT in achieving sustainability goals by reducing environmental degradation and improving economic growth and human development. Moreover, these empirical results may draw the attention of policymakers as they help them build rigorous economic policies to sustain economic development.

In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective of normal form theory. A computer simulation is used to illustrate the analytical results.

We investigate chaos control and hybrid synchronization in a variable-order fractional Arneodo system by treating the differentiation order $\alpha \left(t\right)$ as a closed-loop control variable. A hybrid chaos indicator, combining a tracking error with a windowed estimate of the largest Lyapunov exponent, drives both static and dynamic order modulation laws. The presence and uniqueness of solutions are demonstrated through two distinct methodologies: a piecewise constant-order decomposition with an explicit convergence rate and a direct contraction-mapping argument on the variable-order Volterra operator. Local stability is analyzed via Matignon’s spectral criterion under a quasi-static (frozen-time) approximation. The modulation laws are designed to steer $\alpha \left(t\right)$ below the critical order ${\alpha }_c\approx 0.8632$, at which the nontrivial equilibria $E_{1,2}=(\pm \sqrt{5.5},0,0)$ become locally asymptotically stable. A second-order predictor–corrector scheme attains its expected convergence rate. A controlled ablation study over 200 Monte Carlo runs demonstrates that the proposed laws reduce the terminal tracking error by 81% relative to the best fixed-order baseline, while requiring approximately eight orders of magnitude less control effort than classical active control. Hybrid synchronization (complete in $(u,v)$ and anti-synchronization in w) is successfully achieved in the variable-order setting.

This study examines a comprehensive class of coupled nonlinear $\varrho$-Hilfer fractional neutral impulsive integro-differential systems with mixed delays and non-local initial conditions. The primary contribution of this study is the creation of a unified analytical framework that encompasses coupled interactions, neutral-type dependencies, and impulsive disturbances, which have been studied separately by researchers. We utilize the Banach contraction principle and Krasnoselskii’s fixed-point theorem to provide suitable conditions for the existence and uniqueness of solutions within the product space of piecewise continuous weighted functions. In addition to existence, we examine Ulam–Hyers–Rassias (UHR) stability using a generalized Gronwall inequality, which guarantees the system’s robustness against functional perturbations. We also develop a controllability framework and a feedback control law that steer the system towards the desired terminal states. The theoretical results are supported by a numerical simulation using a complex kernel, implemented via a modified predictor-corrector algorithm, which validates the practical effectiveness of the proposed control and stability outcomes.

In this article, we discuss the findings of new developments in a class of new triangular functions that blend the quantity functions of the traditional triangular. Considering the significant role played by the triangular functions in applied mathematics, physics, and engineering, it is conceivable to predict that the theory of new triangular functions will provide us with additional interpretations and discoveries in mathematics and physics. The solutions which consider variable separation based on arbitrary functions are constructed to the (3+1)-dimensional Burgers model by presenting the Fibonacci Riccati technique and the linearly independent variable separation approach. This technique’s fundamental concept is to describe the solution of the Burgers model as a polynomial in the Riccati Equation solution that satisfies the symmetrical hyperbolic and triangular Fibonacci functions. Depending on the choice of suitable functions for variable separation, an abundance of new localized solutions were obtained. Moreover, examples such as embedded solitons, rectangle-solitons, plateau-type ring solitons, taper-like solitons, and their interactions with each other, following the symmetrical hyperbolic and triangular Fibonacci functions, as well as the golden mean, could be explored.

We study the exact partial controllability of a semilinear stochastic fractional evolution equation of Caputo order $\alpha \in (1,2)$ in a separable Hilbert space, subject to a genuine state-dependent delay $y(t-\rho (t,y_t))$, impulsive effects, and Q-Wiener perturbations. To accommodate the state-dependent delay, we work in a Sobolev-type prehistory space that restores the local Lipschitz property lost in the space of continuous functions, and to accommodate the impulses, we use a piecewise-continuous mean-square path space; two initial data points are prescribed, as required for $\alpha \in (1,2)$. The existence and uniqueness of mild solutions are established by the Banach contraction principle on a Lipschitz ball equipped with a Bielecki-type weighted norm, which removes the smallness conditions of the contraction-based literature. The stochastic convolution is treated rigorously by the Da Prato factorization realized through the subordination of the fractional resolvent family, with the Burkholder inequality applied only to the genuine Itô integral and never to the non-martingale convolution itself. For controllability, we adopt the correct stochastic notion: the target is an ${\mathcal{F}}_T$-measurable random variable, and the adapted control is constructed through the martingale representation theorem, together with the projected controllability Gramian, yielding $Py\left(T\right)=\eta$ almost surely. A numerical study on a stochastic fractional wave equation verifies the main controllability theorem, driving the projected terminal state to the prescribed ${\mathcal{F}}_T$-measurable target at machine precision, and confirms the observability requirement.