In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

Different strategies have been utilized by investigators with the intention of upgrading the thermal characteristics of ordinary liquids like water and kerosene oil. The focus is currently on hybrid nanomaterials since they are more efficient than nanofluids, so as to increase the thermal conductivity of fluids and mixtures. In a similar manner, this investigation is performed with the aim of breaking down the consistent mixed convection flow close to a two-dimensional unstable flow between two squeezing plates with homogeneous and heterogeneous reaction in the presence of hybrid nanoparticles of the porous medium. A sustainable suspension in the ethylene glycol with water is set by dissolving inorganic substances, iron oxide Fe 3 O 4 and cobalt (Co), to form Fe 3 O 4 − Co / C 2 H 6 O 2 − H 2 O hybrid nanofluid. The numerical and analytical model portraying the fluid flow has been planned, and similitude conditions have been determined with the assistance of the same transformations. The shooting technique has been used to solve nonlinear numerical solution. To check the validity of the results obtained from the shooting mode, the Matlab built-in function BVP4c and Mathematica built-in function homotopy analysis method (HAM) are used. The influence of rising parameters on velocity, temperature, skin friction factor, Nusselt number, and Sherwood number is evaluated with the help of graphs and tables. It has been found in this work that to acquire a productive thermal framework, the hybrid nanoparticles should be considered instead of a single sort of nanoparticles. In addition, the velocities of both the hybrid nanofluids and simple nanofluids are upgraded by the mixed convection boundary, whereas they are decreased by the porosity. An augmentation in volumetric fraction of nanoparticles correlates to an increment in the heat transmission rate. It is also found that heat transfer rate for Fe 3 O 4 − Co / C 2 H 6 O 2 − H 2 O hybrid nanofluids (HNF) is better than that of the Fe 3 O 4 − C 2 H 6 O 2 − H 2 O of single nanofluids (SNF). This research shows that hybrid nanofluids play a significant part in the transfer of heat and in the distribution of nanofluids at higher temperatures.

The zoonotic infection campylobacteriosis poses a significant public health burden, contributing to widespread morbidity and, in severe cases, mortality, particularly among vulnerable populations such as children, the elderly, and immunocompromised individuals. The economic impact is considerable, with costs arising from medical care, hospitalization, lost productivity, and the need for stringent food safety measures. In this paper, we model the dynamics of campylobacteriosis with drug resistance in humans and animals using fractional derivatives. The fundamental concepts of fractional derivatives are presented to analyze the disease dynamics. Our work focuses on both the quantitative and qualitative analysis of the proposed model. The fixed-point theorem is applied to investigate the existence and uniqueness of solutions. We also examine the stability of the system through analytical techniques. To further explore the system, a numerical scheme is introduced to visualize the solution pathways and assess the influence of various factors. We demonstrate the dynamics of campylobacteriosis with drug resistance, highlighting the effects of different factors on infection levels. Furthermore, our results identify the key factors crucial for effective disease control and management.

The paper deals with the existence of three different weak solutions of [ ] -Laplacian fractional for an overdetermined nonlinear fractional partial Fredholm–Volterra integro-differential system by using variational methods combined with a critical point theorem due to Bonanno and Marano.

The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is significant for its ability to model complex systems, its contribution to the advancement of mathematical theory, and its wide-ranging applicability to real-world problems. This paper examines the global existence and general decay of solutions to a wave equation characterized by coupling with logarithmic source and delay terms, and governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under a range of hypotheses, and the general decay behavior is established through the construction and application of an appropriate Lyapunov function.