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Recognizing the flow behaviours across a Riga plate can reveal information about the aerodynamic efficiency of aircraft, heat propagation, vehicles, and other structures. These data are critical for optimizing design and lowering drag. Therefore, the purpose of the current analysis is to examine the energy and mass transfer across the mixed convective nanofluid flows over an extending Riga plate. The fluid flow is deliberated under the influences of viscous dissipation, exponential heat source/sink, activation energy, and thermal radiation. The Buongiorno’s concept is utilized for the thermophoretic effect and Brownian motion along with the convective conditions. The modelled are simplified into the lowest order by using similarity transformation. The obtained set of non-dimensional ordinary differential equations is then numerically solved through the parametric continuation method. For accuracy and validation of the outcomes, the results are compared to the existing studies. From the graphical analysis, it can be observed that the fluid velocity boosts with the rising values of the divider thickness parameter. The fluid temperature also improves with the effect of Biot number, Eckert number, and heat source factor. Furthermore, the effect of heat source sink factor drops the fluid temperature.

In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM). The two suggested approaches are briefly explained, along with how to use them to solve the fractional Hirota–Satsuma coupled KdV problem. Some analytical approximate solutions for the current problem are derived using the proposed techniques until the second-order approximation. To ensure high accuracy of the derived approximation, they are analyzed numerically and graphically and compared with the exact solutions of the integer cases. The offered techniques demonstrate more accuracy in their outcomes compared to other alternatives. The numerical results show that ARPSM and ATIM are highly accurate, practical, and beneficial for solving nonlinear equation systems. The current results are expected to help many physics researchers in modeling their different physical problems, especially those interested in plasma physics.

The fractional-order differential equations (FO-DEs) faithfully capture both physical and biological phenomena making them useful for describing nature. This work presents the stable and more effective closed-form traveling-wave solutions for the well-known nonlinear space–time fractional-order Burgers equation and Lonngren-wave equation with additional terms using the exp(−Φ(ξ))(-\Phi (\xi )) expansion method. The main advantage of this method over other methods is that it provides more accuracy of the FO-DEs with less computational work. The fractional-order derivative operator is the Caputo sense. The transformation is used to reduce the space–time fractional differential equations (FDEs) into a standard ordinary differential equation. By putting the suggested strategy into practice, the new closed-form traveling-wave solutions for various values of parameters were obtained. The generated 3D graphical soliton wave solutions demonstrate the superiority and simplicity of the suggested method for the nonlinear space–time FDEs.

In this research study, we focus on the generalized regularized long wave equation and the modified regularized long wave equation, which play pivotal roles in characterizing plasma waves in oceans and ion acoustic waves in shallow water, a domain deeply rooted in physical phenomena. Employing two computational techniques, namely, the optimal auxiliary function method and the Laplace iterative transform method, we approximate these equations. These formulas are used to characterize plasma waves in oceans and ion acoustic waves in shallow water. The results discovered have important ramifications for our comprehension of many physical events. Our results show that both methods are robust, easy to use, and successful. Both methods yield results that are satisfactory to each other. With the use of tables and graphs, we compared the two suggested approaches. The findings suggest that the suggested methods can be widely applied to explore other real-world problems.

This study examines the heat transfer properties of a recently created hybrid nanofluid in contrast to a traditional nanofluid. The aim is to improve the transfer of heat in the flow of the boundary layer by employing this novel hybrid nanofluid. Our study investigates the impact of the Lorentz force on a three-dimensional stretched surface. We utilize a new model that incorporates thermo-physical factors. A quantitative parametric study is performed to investigate the influence of different physical parameters, enabling meaningful comparisons. The results demonstrate that the hybrid nanofluid exhibits a higher heat transfer rate compared to the conventional fluid, even in the presence of a magnetic field. Moreover, the efficiency of heat transfer can be enhanced by modifying the concentration of nanoparticles in the hybrid nanofluid.

The fractional structures of variables using Riemann–Liouville notion have been analyzed by various authors. The novel idea of this article is to introduce the new notion of weighted behavior on random variables using integral inequalities. In view of these, we obtain some new generalized fractional inequalities by using this new fractional integration of continuous random variables.

The optimal auxiliary function method (OAFM) is introduced and used in the analysis of a nonlinear system containing coupled Schrödinger–KdV equations, all within the framework of the Caputo operator. The OAFM, known for its efficiency in solving nonlinear issues, is used to obtain approximate solutions for the coupled equations’ complicated dynamics. Numerical and graphical assessments prove the suggested method’s correctness and efficiency. This study contributes to the understanding and analysis of coupled Schrödinger–KdV equations and their many applications by providing insights into the behavior of nonlinear systems within mathematical physics.

In this research paper, the authors aim to establish a novel algorithm in the finite difference method (FDM). The novel idea is proposed in the mesh generation process, the process to generate random grids. The FDM over a randomly generated grid enables fast convergence and improves the accuracy of the solution for a given problem; it also enhances the quality of precision by minimizing the error. The FDM involves uniform grids, which are commonly used in solving the partial differential equation (PDE) and the fractional partial differential equation. However, it requires a higher number of iterations to reach convergence. In addition, there is still no definite principle for the discretization of the model to generate the mesh. The newly proposed method, which is the SM method, employed randomly generated grids for mesh generation. This method is compared with the uniform grid method to check the validity and potential in minimizing the computational time and error. The comparative study is conducted for the first time by generating meshes of different cell sizes, i.e., 10×10,20×20,30×30,40×4010\times 10,\hspace{.25em}20\times 20,\hspace{.25em}30\times 30,\hspace{.25em}40\times 40 using MATLAB and ANSYS programs. The two-dimensional PDEs are solved over uniform and random grids. A significant reduction in the computational time is also noticed. Thus, this method is recommended to be used in solving the PDEs.

The symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. The generalized form of the fractional differential equations is the variable-order fractional differential equations that describe the physical and biological applications. This paper discusses the closed-form traveling wave solutions for the nonlinear space-time variable-order fractional modified Kawahara and (2 + 1)-dimensional Burger hierarchy equations. The variable-order fractional differential equation has a derivative operator in the Caputo sense that is converted into the integer-order ordinary differential equation (ODE) by fractional transformation. The obtained ODE is solved by the exponential rational function method, and as a result, new exact solutions are constructed. Two problems are proposed to confirm the solutions of the space-time variable-order fractional differential equations. [ABSTRACT FROM AUTHOR]

This research paper aims to investigate the peristaltic transport of a nanofluid (NF) in a tapered asymmetric channel. Initially, the governing equations for the balance of mass, momentum, temperature, and volume fraction for the NF using Reiner–Philippoff (RP) based NF are formulated. Subsequently, these equations are employed to analyze long wavelength and small Reynolds number scenarios. The numerical results for various flow features are thoroughly examined and discussed. Dual solutions have been examined for some factors. So, stability assessment is implemented to find stable solution. Novelty of the existing is to investigate the peristaltic motion of Buongiorno's NF model and its stability which has not investigated in the previous literatures. It has been demonstrated that modifying the RPF parameter leads to a transition in the fluid's velocity, changing it from a dilatant liquid to a Newtonian fluid and from Newtonian to pseudoplastic. The findings indicate that the temperature curves rise as Brownian motion and thermophoretic factors increase, while they decrease as the Prandtl number increases. Furthermore, a concise mathematical and graphical analysis is carried out to examine the impact of each key parameter on the flow characteristics. [ABSTRACT FROM AUTHOR]

This study delved into the dynamics of wave solutions within the Estevez-Mansfield-Clarkson equation in fractional nonlinear space-time. Utilizing conformable fractional derivatives, the equation governing shallow water phenomena and fluid dynamics was transformed into a nonlinear ordinary differential equation. Applying the Riccati Bernoulli sub-ODE approach yielded a finite series representation. Notably, our findings revealed novel solitary wave solutions characterized by kink, anti-kink, periodic, and shock functions. Visualized through 3D and contour graphs, kink and periodic waves emerged as distinct observable manifestations. Intriguingly, the diversity of results surpassed previous results, contributing to a deeper understanding of the intricate dynamics inherent in the system. [ABSTRACT FROM AUTHOR]

The complex Hirota-dynamical model (CHDM) has applications in the study of plasma physics, the investigation of fusion energy, astrophysical research, and space studies. The CHDM may also be used to investigate turbulent flows to study shocks and other nonlinear phenomena, and light waves venturing through the fibers. Nowadays, plasma physics, fusion energy, astrophysical research, and space studies are very interesting topics in the modern research. So, we need to shed light on this model as a good application in these fields. For deep investigation of these physical problems, we need to find their analytical solutions. In this study, we explore a variety of soliton solutions with different geometrical structures for the CHDM via the double variable expansion method. By means of this method, we have obtained three types of soliton solutions, namely, hyperbolic, trigonometric, and rational function solutions. The graphical interpretation of these solutions gives us some popular shapes such as singular-periodic, kink, bell, and singular shapes. The performed method is an efficient technique to execute and provides reliable analytical soliton solutions which are very important to further advanced investigation of the mention equation. [ABSTRACT FROM AUTHOR]

In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains. [ABSTRACT FROM AUTHOR]