The study consists of the distinct types of the exact soliton solutions to an important model called the beta-time fractional (1 + 1)-dimensional non-linear Van der Waals equation. This model is used to explain the motion of molecules and materials. The Van der Waals equation explains the phase separation phenomenon. Noncovalent Van der Waals or dispersion forces usually have an effect on the structure, dynamics, stability, and function of molecules and materials in different branches of science, including biology, chemistry, materials science, and physics. Solutions are obtained, including dark, dark-singular, periodic wave, singular wave, and many more exact wave solutions by using the modified extended tanh function method. Using the fractional derivatives makes different solutions different from the existing solutions. The gained results will be of high importance in the interaction of quantum-mechanical fluctuations, granular matters, and other applications of the Van der Waals equation. The solutions may be useful in distinct fields of science and civil engineering, as well as some basic physical ones like those studied in geophysics. The results are verified and represented by two-dimensional, three-dimensional, and contour graphs by using Mathematica software. The obtained results are newer than the existing results. Stability analysis is also performed to check the stability of the concerned model. Furthermore, modulation instability is studied to study the stationary solutions of the concerned model. The results will be helpful in future studies of the concerned system. In the end, we can say that the method used is straightforward and dynamic, and it will be a useful tool for debating tough issues in a wide range of fields.

This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; and all parameters are estimated and fitted. Subsequently, the basic reproductive number is determined, and subpopulation trends are observed over time. Sensitivity analysis is conducted to identify critical drivers influencing transmission dynamics. Two-dimensional plots visualize the impact of crucial parameters on the reproductive number. Through a comprehensive literature review and case analysis, an association between Lassa fever and various disabilities is established, including conditions such as encephalitis, hearing loss, ataxia, neuropsychiatric manifestations, meningitis, seizures, and coma. Solutions are devised and analyzed to enhance early detection, treatment, and mitigation of disease.

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hybrid weighted arithmetic averaging aggregation operator, and demonstrate several essential characteristics of the aforementioned aggregation operators. Furthermore, we provide a multi attribute decision-making approach and the technique of the suggested approach in the context of the intuitionistic hesitant fuzzy rough set. A real-world problem for selecting a suitable worldwide partner for companies is employed to demonstrate the effectiveness of the suggested approach. The sensitivity analysis of the decision-making results of the suggested aggregation operators are evaluated. The demonstrative analysis reveals that the outlined strategy has applicability and flexibility in aggregating intuitionistic hesitant fuzzy rough information and is feasible and insightful for dealing with multi attribute decision making issues based on the intuitionistic hesitant fuzzy rough set. In addition, we present a comparison study with the TOPSIS approach to illustrate the advantages and authenticity of the novel procedure. Furthermore, the characteristics and analytic comparison of the current technique to those outlined in the literature are addressed.

This paper analyzes and examines the ion sound and Langmuir waves (ISALWs) model with noise term utilizing the powerful extended tanh technique and the complete discrimination system for the polynomial method. Namely, we introduce some new stochastic solutions for the ISALWs model with multiplicative noise in the Itô sense. Ion sound waves and Langmuir waves are distinguished as fundamental plasma waves, characterized by varying frequencies, wavelengths, and modes of propagation. The combination of ion inertia and electron pressure results in the propagation of low-frequency electrostatic waves, referred to as ion sound waves, within a plasma. Langmuir waves refer to the high-frequency electrostatic oscillations of electrons within a plasma, while ions, due to their larger mass, are considered to be almost at rest. We also investigate how the noise term affects the structural characteristics of waves. These results have potential relevance to plasma physics applications, such as solar wind dynamics, Langmuir turbulence, and burst-like wave phenomena in cusp regions. Utilizing the capabilities of the MATLAB release, several profile pictures are created to demonstrate the behavior of the presented stochastic solutions. Ultimately, the suggested methodology has the potential to be adapted for various other models in the applied science.

This paper aims to obtain exact solutions of solitary waves for the conformable fractional Sharma-Tasso-Olver (STO) equation which plays an important role in nuclear physics to describe the physical occurrences such as the fission and fusion processes. Solitary waves operate central parts in different areas of study such as electromagnetism, atomic quantum theory, as well as special relativity. By means of sub-ode approach with the aid of the modified fractional Riccati-Bernoulli equation, the exact forms of generalized solitary solution of the fractional (STO) equation are found and specified in hyperbolic, trigonometric, and rational functions. This makes the visualization of the fractional effects and the dynamic behaviors of these solutions in 3D and 2D help in establishing practicality for application of the results. The novel analytical results benefit general engineering and mathematical physics in demonstrating that the proposed employment of the given technique allows solving nonlinear problem analytically. These findings are significant for the progress of wave proceedings in the number of applications.