El Shorouk Academy

This study presents a comprehensive investigation of exact fractional wave solutions and bifurcation analysis for the (3 + 1)-dimensional extended shallow water wave (3D-eSWW) equation with β-derivative, which models nonlinear wave phenomena in fluid dynamics and coastal engineering. Leveraging the flexibility of the fractional derivative, the model provides a more generalized and adaptable framework for describing shallow water wave propagation. The Modified Extended Direct Algebraic Method (MEDAM) is systematically employed to derive a broad spectrum of novel exact analytical solutions. These include the following: dark solitary waves, singular solitons, singular periodic waves, periodic solutions expressed via trigonometric and Jacobi elliptic functions, polynomial solutions, hyperbolic wave patterns, combined dark–singular structures, combined hyperbolic–linear waves, and exponential-type wave profiles. Each solution family is presented with explicit parameter constraints that ensure both mathematical consistency and physical relevance, thereby offering a robust classification of wave regimes under diverse conditions. A thorough bifurcation analysis is conducted on the reduced dynamical system to examine parametric dependence and stability transitions. Critical bifurcation thresholds are identified, and distinct solution branches are mapped in the parameter space spanned by wave numbers, nonlinear coefficients, external forcing, and the fractional order β. The analysis reveals how solution dynamics undergo qualitative transitions—such as the emergence of solitary waves from periodic patterns or the appearance of singular structures—driven by the interplay of nonlinearity, dispersion, and fractional-order effects. These insights are crucial for understanding wave stability, predictability, and the onset of extreme events in shallow water contexts. Graphical representations of selected solutions validate the analytical results and illustrate the influence of β on wave morphology, propagation, and stability. The simulations demonstrate that varying the fractional order can significantly alter wave profiles, highlighting the role of fractional calculus in capturing complex real-world behaviors. This work demonstrates the efficacy of the MEDAM technique in handling high-dimensional fractional nonlinear PDEs and provides a systematic framework for predicting and classifying wave regimes in real-world shallow water environments. The findings not only enrich the solution inventory of the 3D-eSWW equation but also advance the analytical toolkit for studying complex spatio-temporal dynamics in fractional mathematical physics and fluid mechanics. Ultimately, this research contributes to the development of more accurate models for coastal protection, tsunami forecasting, and marine engineering applications.

In this work, we present a comprehensive analytical investigation of the [Formula: see text]-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation, a higher-dimensional nonlinear evolution equation of significant relevance to fluid dynamics and wave propagation. By employing two robust analytical techniques, the enhanced modified extended tanh expansion method and the unified method, we construct a diverse class of exact solutions, including bright, dark, periodic, and rational wave structures. These solutions are illustrated using three-dimensional surface plots, two-dimensional profiles, and contour maps to capture their dynamic behaviors and physical characteristics. Furthermore, a detailed bifurcation analysis is conducted to investigate the system’s qualitative dynamics under varying parameter regimes. Phase portraits are employed to illustrate transitions between equilibrium states and to characterize the stability and bifurcation structures. A sensitivity analysis is also performed to assess the model’s robustness with respect to parameter variations. Overall, the findings contribute new insights into the nonlinear dynamics and integrability properties of higher-dimensional evolution equations, broadening the current understanding of complex wave phenomena.

In this article, we introduce an enhanced version of the log-logistic model, termed the Kumaraswamy alpha-power log-logistic (KAPLL) distribution. The KAPLL model expands upon the traditional log-logistic distribution and several well-established distributions. We investigate the mathematical properties of the KAPLL model, highlighting its ability to effectively model various aging and failure criteria. The KAPLL distribution exhibits remarkable flexibility in modeling various types of hazard rate behaviors. It is capable of accommodating a wide range of shapes, including increasing, decreasing, J-shaped, reversed J-shaped, bathtub-shaped, inverted bathtub-shaped, and even more complex forms such as decreasing–increasing–decreasing failure rates. The KAPLL distribution is characterized by its capacity to exhibit both symmetric and asymmetric shapes in its density function. The proposed KAPLL model overcomes key limitations of existing LL-based generalizations by offering enhanced flexibility in modeling diverse hazard rate shapes and tail behaviors. We estimate the KAPLL parameters using eight classical estimation methods. Comprehensive simulation results are presented and ranked to identify the most effective approach for estimating KAPLL parameters, which we believe will be of great interest to engineers and applied statisticians. To further demonstrate the versatility of the KAPLL distribution, we analyze five real-world datasets from reliability, engineering, biomedical, and environmental sciences, highlighting its flexibility relative to other extensions of the log-logistic model. Likelihood ratio tests conducted across five real datasets confirm that the KAPLL model provides a statistically significant improvement over the baseline log-logistic distribution.

Speed tracking control (STC) and energy saving of an electric vehicle (EV) play a crucial role in the stability and effectiveness of the operating performance of an EV drive system (EVDS). This paper proposes a novel STC and energy saving methodology for an EVDS that is tested by the European drive cycle (ECE-15) and customized inspection and maintenance drive cycle (custom IM240). The EVDS adopted the 5-ph interior permanent magnet synchronous motor (IPMSM) due to its benefits like high efficiency, compact size, low noise, reliability, reduced torque ripples, increased power density, and improved fault tolerance. A multilayer perceptron (MLP) - artificial neural network (ANN) is utilized to tune the PI controller online in the drive system (DS). The gating pulses of the 5-phase voltage source inverter (VSI) are accurately generated using an MPC based on a desired cost function to reduce current harmonics and thus torque ripples. A comparative study between the online tuning using the MLP-ANN and offline tuning using the transit search optimization (TSO) technique is presented. The process of comparison includes the percentage overshoot, mean square error (MSE), integral absolute error (IAE), and percentage energy saving. The result of the comparison proves the effectiveness of the proposed control methodology that gives superior speed tracking performance of the EVDS and attains energy saving. The attained energy saving across a long period results in cost reduction of charging the batteries and increasing their lifetime.

Geo-polymer concrete (GPC) is a type of eco-friendly concrete that may reduce the emission of a lot of carbon dioxide (CO2) in the atmosphere and thus represents an alternative to the cement matrix. This research investigates the effect of percent of recycled aggregate replacement and super plasticizer dosage on workability, compressive strength, tensile strength, and flexural strength of self-compacting slag-based geo-polymer concrete containing recycled aggregate. Self-Compacting Geo-Polymer Concrete (SCGC) is an advanced method of concrete placement that eliminates the need for compaction and is produced without using any ordinary Portland cement. The parameters that were studied are the recycled aggregate percentage and super plasticizer dosage. Four slag-based geo-polymer concrete mixtures were examined. The workability properties such as filling ability and segregation resistance were examined by using slump flow, L-box, V-funnel test methods. The results revealed that an increase in strength and a decrease in workability of these concrete samples were observed with the increase in superplasticizer dosage.

This paper investigates new optical soliton solutions to the complex Ginzburg-Landau equation in the presence of white noise, a fundamental model in nonlinear optics that describes soliton dynamics. The study focuses on nine distinct forms of self-phase modulation structures, each exhibiting unique nonlinear characteristics and dispersion properties. To derive the soliton solutions, the generalized -expansion approach is employed, which is known for its effectiveness in handling nonlinear differential equations and extracting exact solutions systematically. Through this analytical framework, a variety of soliton profiles are retrieved, demonstrating the influence of nonlinear dispersion and gain-loss terms on soliton propagation. A key observation from the analysis is that the presence of white noise primarily affects the phase component of the solitons, while their amplitude remains intact. This result suggests that the robustness of the soliton amplitude against stochastic perturbations could have significant implications for practical optical communication systems and laser pulse propagation, where maintaining stable intensity profiles is crucial. The obtained results provide valuable insights into the interplay between noise and nonlinear wave dynamics, offering potential applications in fiber-optic communication, mode-locked lasers, and other areas of photonics where controlled soliton evolution is essential.•The paper investigates optical soliton solutions of the complex Ginzburg-Landau equation with white noise, focusing on nine forms of self-phase modulation with varied nonlinear and dispersive properties.•Using the generalized -expansion method, the study derives exact soliton profiles, revealing how nonlinear dispersion and gain-loss mechanisms shape soliton dynamics.•A key finding shows that white noise affects soliton phase without disturbing amplitude, highlighting amplitude robustness with implications for optical communications and laser systems.