In this paper, we study the nonlinear wave propagation of the fractional Joseph-Egri equation by means of the modified Sardar sub-equation method. The non-linear model under consideration includes Riemann-Liouville fractional derivatives, which are efficient in reflecting memory and heredity phenomena that are often present in complex physical media, such as polymers, gels, and biological tissues. With the aid of a proper traveling wave transformation, we reduce the non-linear partial differential equation to an ordinary differential equation. Finally, we use the modified Sardar sub-equation method to obtain various non-linear solutions, including bright soliton, dark soliton, dark singular soliton, periodic singular, and rational waves. By means of graphical analysis, we examine the effect of the fractional parameters alpha and beta on the non-linear solutions. In order to further validate the accuracy of the analytical results, numerical approximations of the solution have been carried out by employing the differential transform method, which has revealed an excellent agreement between the exact and numerical results with very small absolute errors. Moreover, an analysis of modulation instability is carried out in order to validate the stability of the background wave. The results have shown that the perturbation frequency is real for the considered parameter condition, thus validating that the system is modulationally stable. The results have revealed that fractional derivatives play an important role in governing wave attenuation, dispersion, and localization in viscoelastic media, thus providing more insight into nonlinear wave propagation in complex systems. The novelty of the study lies in the application of the modified Sardar sub-equation method, which provides a systematic and efficient framework for generating a wide variety of exact nonlinear wave solutions. Unlike many conventional analytical techniques that yield limited solution structures, the proposed approach enables the construction of bright, dark, singular, periodic, and rational wave solutions within a unified formulation.
LuFeO3 (LFO) is a perovskite oxide with promise for optical and electroceramic applications. In the present study, LFO and Co-substituted compositions (LFO, LuFe0.95Co0.05O3, and LuFe0.90Co0.10O3) were synthesized by a conventional solid-state route and characterized by SEM, Raman spectroscopy, diffuse reflectance, and broadband dielectric/impedance measurements. Co substitution alters the powder microstructure, yielding more irregular agglomerates composed of finer sub-units than undoped LFO. Dielectric spectra showed that the loss tangent (tanδ), the dissipation factor, of investigated samples was below 1 over the studied temperature–frequency window. It was seen that Co substitution decreased dielectric loss in the mid-to-high frequency region but raised low-frequency loss at advanced temperatures. The real part of impedance Z^' declined with both temperature and frequency, and Nyquist plots displayed depressed arcs, indicating non-Debye behavior with distributed grain and grain-boundary contributions. Arrhenius analysis of relaxation maxima yielded activation energies of ∼ 0.32–0.76 eV, consistent with oxygen-vacancy energies. Raman spectra revealed Co-induced lattice perturbations, including mode broadening/attenuation and red-shifts in the 200–600 cm− 1 range, together with a strengthened stretching feature near 600–650 cm− 1. Kubelka–Munk analysis was utilized to determine the band gaps of the studied samples, 2.19 eV (LFO), 2.29 eV (5
This study uses the Levenberg-Marquardt strategy with feed forward neural networks (LMS-FNN) to inspect the Soret-Dufour effect on radiative hybrid nanofluid flow across a Riga plate with gyrotactic microorganisms. The suggested model, which investigates the thermal behavior of bioconvection flow in CNTs/water based hybrid nanofluid, gyrotactic microbes, when considered alongside Soret-Dufour impact, contribute notably to important uses in biotechnology, energy systems, and industrial heat management. It is important to optimize bioreactors that require high microbial activity and heat transfer, to improve the design of innovative cooling systems that use hybrid nanofluid, and to aid in the creation of efficient microfluidic devices. Artificial neural networks provide accurate prediction of complex fluid-microbe interactions, which aids in the design and control of next-generation thermal and bioengineering processes. From reference results, execute LMS-FNN validation, training, and testing to get approximated solutions for variations connected with the physical system and to demonstrate the correctness of the suggested LMS-FNN. The Mean squared error, histograms, and regression analysis are used to examine the performance of LMS-FNN, and the problem is satisfactorily solved. The microorganism profile profile declines as the Peclet number increases.
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 ( R_0 ) 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 R_0 oscillating before settling between 3 and 7. Three-dimensional parameter surfaces further identified combinations of vector control and treatment coverage sufficient to reduce R_0 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.
OBJECTIVE:Elevated serum creatine kinase (CK) levels, or hyperCKemia, are frequently observed in pediatric patients with muscle weakness, fatigue, or gait abnormalities. Although often associated with neuromuscular disorders (NMD), CK elevation may also result from non-neuromuscular causes such as infection, trauma, exercise, or systemic illness. This study aimed to investigate the underlying causes and clinical features of pediatric patients referred with symptomatic CK elevation. MATERIALS AND METHODS:In this retrospective cohort study, 1,688 pediatric patients with symptomatic hyperCKemia (CK>200 U/L) were analyzed. Patients were categorized into NMD and non-NMD groups and stratified by CK severity: mild (<2000 U/L) and moderate to severe (≥2000 U/L). Symptomatic cases were further classified as acute sporadic, hereditary neurometabolic/genetic, hereditary neuromuscular, or non-hereditary/chronic cases. RESULTS:The cohort included 27.2% female and 72.8% male, with a mean age of 7.4 years. The mean CK level was 1615.1 ± 5390.7 U/L (range: 201-121480), with moderate-to-severe hyperCKemia in 12.7%. CK showed a weak positive correlation with age (r=0.146, P < .001) and was significantly higher in male (P = .020). Acute sporadic cases constituted 67.2% (n=1134), predominantly infections (17.5%) and trauma (14.7%). Hereditary neurometabolic/genetic cases accounted for 2.4% (n=41), hereditary neuromuscular for 5.4% (n=91), and non-hereditary/chronic cases for 25.0% (n=422). Detailed NMD was detected in 7.5%, with significantly higher CK, and NMD diagnosis rose to 33.2% at CK ≥2000 U/L. CONCLUSION:This study demonstrates that symptomatic hyperCKemia in pediatric patients has diverse etiologies and emphasizes the importance of clinical correlation and a multidisciplinary diagnostic approach.
