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Graphene has emerged as a highly attractive nanomaterial, characterized by its distinctive thermodynamic, electrical, and mechanical features. These attributes render it ideal for a wide array of purposes across materials research, storing energy, computing, filtering water, and medication. In this study, we investigate the nonlinear thermophoretic wrinkle motion equation describing wave propagation and thermal-driven deformation in graphene sheets. Governing model is -dimensional graphene sheets (GS) equation, focusing on the component heat transfer during thermodynamic motion. The study employs modified generalized exponential differential function method and the improved Cham method. These techniques are employed to analyze the nonlinear behavior of wave propagation in GS, leading to exact wave solutions such as bright, bell, periodic, and twofold waves. The creative application of these analytical techniques provides efficient structures for tackling complex nonlinear theories in mathematical physics, thereby enhancing solution strategies for these equations. This study makes a notable contribution to computational mathematics, material research, and nanotechnology by providing exact solutions and deepening our comprehension of graphene non linear properties. The findings present significant implications, suggesting potential applications in the design of novel materials with customized properties to facilitate technological progress, thereby expanding the frontiers of nanotechnology and materials research.

The Albanian energy sector is highly reliant on hydropower, making the national energy balance vulnerable to seasonal variability and hydrological shocks. This study analyzes quarterly electricity production data for 2012Q1–2025Q3 using Seasonal–Trend decomposition via Loess (STL) and Seasonal Autoregressive Integrated Moving Average (SARIMA) modelling. STL is used to isolate trend and seasonal strength, while a SARIMA(0,1,2)(0,1,1) 4 model is estimated to generate production forecasts for the 2025Q4–2030Q4 horizon (Q = calendar quarter). Results confirm a dominant seasonal component (F S = 0.635) and a recurring seasonal trough in Q3. A post-2022 increase in volatility is reflected in widening 95% prediction intervals, indicating that while the seasonal timing of stress is predictable, the magnitude of future outcomes becomes increasingly uncertain over the medium term. To operationalize this risk, the study implements a hydrological drought stress test on Albania’s quarterly net domestic production (Y p ), using the SARIMA baseline as the reference path. The sensitivity results quantify sizable, seasonally concentrated supply gaps under proportional production shocks (− 10% and − 25%), reinforcing the structural nature of the recurring third-quarter (Q3) deficit and its implications for adequacy and import coverage. The findings inform resilience planning by quantifying the scale and timing of seasonal shortfalls and by motivating diversification and flexibility options that are seasonally complementary to hydropower. In particular, solar PV is discussed as a potential counter-cyclical contributor conditional on scale-up, grid hosting capacity, and balancing resources. The paper concludes that hydropower-centric strategies alone are insufficient for medium-term stability and highlights the role of diversified non-hydro resources, grid-efficiency improvements, and storage in hedging forecasted production troughs and reducing exposure to external balancing needs.

Malaria remains a major global health challenge, particularly in regions where socioeconomic inequalities shape exposure risk and access to prevention. In this study, we propose a novel fractional-order malaria transmission model incorporating social hierarchy, mathematically integrating Caputo, Caputo–Fabrizio, and Atangana–Baleanu operators to account for memory effects, immunity waning, and delayed intervention impacts, and epidemiologically distinguishing low- and high-class populations to quantify the influence of socioeconomic disparities on transmission and control. The basic reproduction number ( ) was derived using the next-generation approach, and sensitivity analysis identified mosquito-to-human and human-to-mosquito transmission probabilities, mosquito recruitment, and mortality as the most influential drivers. Numerical simulations over a 200-day horizon showed that lower fractional orders slowed epidemic growth and prolonged infectious periods, while non-singular kernels produced smoother, more realistic post-peak declines. Socioeconomic differences had a significant impact on outcomes. with low-class populations experiencing up to threefold higher peaks in exposure and infectiousness due to reduced access to care and preventive measures. Model projections revealed daily new cases peaking near 2500 under high transmission, and oscillating before settling between 3 and 7. Three-dimensional parameter surfaces further identified combinations of vector control and treatment coverage sufficient to reduce below one. These findings demonstrate the value of fractional-order modeling for capturing complex malaria dynamics and highlight the need for equity-focused interventions, including strengthened vector control, expanded rapid diagnostics, and improved treatment access in disadvantaged communities, to achieve sustainable reductions in malaria transmission.

The main goal of this paper is to obtain error bounds for parabolic integro-differential equation. The derivation of these bounds is based elliptic and Ritz -Volterra reconstructions introduced by Makridakis and Nochetto 2003 and then extended to Ritz - Volterra reconstruction in case of integro-parabolic differential problems by Reddy and Sinha 2015. We proved optimal order bounds for certain classes semilinear parabolic intergro differential equations. The key points for these estimators can be reduced the numbers of iterations.

This study presents a comprehensive investigation of optical solitary waves governed by a third-order complex modified Korteweg-de Vries (higher-order nonlinear Schrödinger-type, mKdV-NLS) equation incorporating stochastic effects. Initially, the methodology outlines the general procedure of this approach. Subsequently, by applying the traveling waves transformation to the given equation, it is reformulated into nonlinear ordinary differential equations (NLODEs). These NLODEs are then decomposed into their imaginary and real components. Furthermore, the proposed methodology is implemented to derive new solutions for optical solitary waves within the mKdV-NLS type model, encompassing stochastic breather-like waves, singular solitons, periodic waves, and various wave interactions. Additionally, numerical visualizations of the exact analytical solitary waves are provided, facilitating an examination of the stochastic term’s influence on wave dynamics. This study advances the understanding of optical wave behavior and clarifies the effects of stochastic contributions, offering valuable insights for both theoretical studies and practical applications in optics and related fields.

The main goal of this paper is to developed a high-order and accurate method for the solution of one-dimensional of generalized Burgers-Fisher with Numman boundary conditions. We combined between a fourth-order compact finite difference scheme for spatial part with diagonal implicit Runge Kutta scheme in temporal part. In addition, we discretized boundary points by using a compact finite difference scheme in terms of fourth order accuracy. This combine leads to ordinary differential equation which will take full advantage of method of line (MOL). Some numerical experiments presented to show that the combination give an accurate and reliable for solving the generalized Burgers-Fisher problems.

This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme for spatial part combined with implicit-explicit Runge Kutta scheme in temporal are proposed. Furthermore, boundary points are discretized by using a compact finite difference scheme in terms of fourth order accuracy. A key idea for proposed scheme is to take full advantage of method of line (MOL), this is consequently enabling us to use implicit-explicit Runge Kutta method, that are of fourth order in time. We constructed fourth order accuracy in both space and time and is unconditionally stable. This is consequently leading to a reduction in the computational cost of the scheme. Numerical experiments show that the combination of the compact finite difference with IMEX- RK methods give an accurate and reliable for solving the Lotka-Volterra-diffusion.

In this work, we study the A [ α ] – stability of the additive methods of Runge- Kutta kind of orders ranging from 2 up to 4 that will be applied for determining some stiff nonlinear system of the ODEs. Moreover, we find the stability function for the additive Runge-Kutta method and some methods of this type of order 2,3, and 4. Where the method ( A,B 1 ) is A-stable and semi-implicit and method ( A,B 2 ) is explicit. Furthermore, the stiff term is managed by the semi-implicit Runge-Kutta method while no stiff term is treated by the explicit Runge Kutta method. Those methods are suitable for solving chemical reactions problems that include stiff and non-stiff terms.

In this article, we deal with statistical estimation problems of drift parameters of a Vasicek-type model that is perturbed by Gaussian noise that is defined via d z t = ϑ ( ν - z t ) d t + d G t , t ⩾ 0 , z 0 = 0 with unknown parameters ϑ > 0 and ν ∈ R , where G is a Gaussian process with index α ∈ ( 0 , 1 ) . Based on discrete observations and using tools from Malliavin calculus together with Nordin–Peccati analysis, we provide estimators ϑ ^ of ϑ and ν ^ of ν . Moreover, the strong consistency and asymptotic normality of our estimators have been established using the properties of G . The rates of convergence in total variation for a sequence of random variables living in a fixed Wiener chaos are computed. Finally, we discuss the case when the process G is replaced by a fractional Brownian motion.

In this article, new multiple-production systems based on the micro-combined cooling, heating and power (CCHP) cycle with biomass heat sources are presented. In this proposed system, absorption refrigeration cycle subsystems and a water softener system have been used to increase the efficiency of the basic cycle and reduce waste. Comprehensive thermodynamic modeling was carried out on the proposed system. The validation of subsystems and the optimization of the system via the genetic algorithm method was carried out using Engineering Equation Solver (EES) software. The results show that among the components of the system, the dehumidifier has the highest exergy destruction. The effect of the parameters of evaporator temperature 1, ammonia concentration, absorber temperature, heater temperature difference, generator 1 pressure and heat source temperature on the performance of the system was determined. Based on the parametric study, as the temperature of evaporator 1 increases, the energy efficiency of the system increases. The maximum values of the energy efficiency and exergy of the whole system in the range of heat source temperatures between 740 and 750 K are equal to 74.2% and 47.7%. The energy and exergy efficiencies of the system in the basic mode are equal to 70.68% and 44.32%, respectively, and in the optimization mode with the MOOD mode, they are 87.91 and 49.3, respectively.