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This research explores new soliton solutions to the Atangana–Baleanu derivative (ABD) fractional system of equations for ion sound and Langmuir waves (FISLW). We utilize the fractional ABD operator to convert our system into an ordinary differential equations. In recent years, machine learning (ML) evolves significantly in the context of data analysis and computing different solutions, which typically enables systems to operate wisely. Now, we are going to use numerous ML tools including matplotlib. pyplot as plt, scipy.integrate, mpl toolkits.mplot3d, and Axes3D to generate various types of optical solutions by using complete discriminant of the polynomial method. We will also analyze solutions for the hyperbolic function, trigonometric function, Jacobian elliptic function (JEF), and other solitary wave solutions. Solitons have extensive uses in pure and applied mathematics, including nonlinear partial differential equations: the Boussinesq equation, the nonlinear Schrödinger equation, and the sine-Gordon equation, Lie groups, Lie algebras, and differential and algebraic geometry. In addition, we study the chaotic behaviour, i.e., 2D, 3D, time series, Poincarè maps, and sensitivity analysis of our governing model. Sensitivity analysis explores how changes in a system’s variables affects its behaviour.

Soliton solutions of the Konopelchenko–Dubrovsky (KD) equation using four analytical methods are established. The KD system is used to study the portrays in physics with weak dispersion. The investigated results are obtained in different forms such as trigonometric, hyperbolic, and exponential functions. For the physical behavior of the concerned nonlinear system, some solutions are plotted graphically via assigning the certain values to the parameters. Mathematica software 11.11 is used to handle all results as well as figures. Hence, searched results have rewarding recompenses in nonlinear science.

The Phi-Four (also embodied as ∅4) equation (PFE) is one of the most significant models in nonlinear physics, that emerges in particle physics, condensed matter physics and cosmic theory. In this study, propagating soliton solutions for the PFE were obtained by employing the extended direct algebraic method (EDAM). This transformational method reformulated the model into an assortment of nonlinear algebraic equations using a series-form solution. These equations were then solved with the aid of Maple software, producing a large number of soliton solutions. New families of soliton solutions, including exponential, rational, hyperbolic, and trigonometric functions, are included in these solutions. Using 3D, 2D, and contour graphs, the shape, amplitude, and propagation behaviour of some solitons were visualized which revealed the existence of kink, shock, bright-dark, hump, lump-type, dromion, and periodic solitons in the context of PFE. The study was groundbreaking as it extended the suggested strategy to the PFE that was being aimed at, yielding a significant amount of soliton wave solutions while providing new insights into the behavioral characteristics of soliton. This approach surpassed previous approaches by offering a systematic approach to solving nonlinear problems in analogous challenging situations. Furthermore, the results also showed that the suggested method worked well for building families of propagating soliton solutions for intricate models such as the PFE. [ABSTRACT FROM AUTHOR]

Nanofluids with variable viscosity have shown tremendous potential in the thermal optimization of many industrial systems. They have seen substantial development in energy applications in recent years. Motivated by these considerations, an analysis has been carried out to investigate the nanofluid flow with temperature dependent viscosity and magnetohydrodynamic (MHD) over a stretched surface. Moreover, heat transfer has effectuated for propylene glycol (C3H8O2) based fluid with nanoparticles silicon dioxide (SiO2), and molybdenum disulfide (MoS2), by heat dissipation and internal heat source/sink. The governing model comprises of non‐linear partial differential system (PDE). Suitable transformations are executed to convert the governing system into non‐similar dimensionless form. The transformed non‐similar PDEs are estimated by ordinary differential equations (ODEs) with the approximations of local non‐similarity (LNS) approach. Numerical simulations are performed using computational algorithm bvp4c. The key findings include that significance of distinct physical parameters on fluid flow and thermal transport which are revealed through graphs and tables. It is noted that by upsurging magnetic parameter, velocity of fluid reduces while temperature profile enhances. Moreover, velocity profile lessens by enlarging temperature dependent viscosity parameter. Enhancement in nanoparticles fraction upsurges the temperature and velocity profiles. Rising estimations of the Brinkman number, Biot number, and heat generation parameter uplift the temperature profile. Furthermore, a comparison is designed to check the accuracy of applied approach with existing literature. The range of various physical parameters are also calculated. [ABSTRACT FROM AUTHOR]

In this study, we give the stability analysis of a class of nonlinear systems with a generalized conformable derivative, which guarantees that their solutions converge to a ball centered at the origin. The theoretical foundations of the practical stability are investigated in this work. Furthermore, the concept is elucidated with an application. Finally, the theoretical findings offered are illustrated with two numerical examples. [ABSTRACT FROM AUTHOR]