Nonlinear periodic structures in magnetoplasma with nonthermal electrons and positrons

In the present study, we address the problem of cnoidal waves (CWs) in magnetized electron-positron-ion (e-p-i) plasma with nonthermal electrons and positrons. The Korteweg-de Vries equation (KdVE) is derived using the reductive perturbation technique (RPT) and its cnoidal wave (CW) solution is analyzed. The impact of relevant plasma parameters on the characteristics of the ion-acoustic (IA) cnoidal structures are discussed in detail. The application of the present investigation is discussed

THE UP-GRATING RANK APPROACH TO SOLVE THE FORCED FRACTAL DUFFING OSCILLATOR BY NON- PERTURBATIVE TECHNIQUE

The current research studies a fractal Duffing oscillator in the presence of periodic force. To find an analytic solution for this oscillator, the aspects explained in the following are considered. First, we obtain an alternative unforced fractal fourth-order equation and then convert it into a continuous space. Therefore, the non-perturbative (NP) approach is used to calculate the analytic solution for the alternate equation in the second-order form after reducing its rank. It is seen that the analytical and numerical solutions agree very well. The computations reveal that for every value of the fraction parameter, the approximation and numerical solutions are identical. The present study gives reliability in the technique of reducing the order of differential equations. Furthermore, the required periodic solution is also obtained by Galerkin’s technique. In contrast to the traditional technique, which works to transform the variable and is valid only in the absence of external forces, if there is an external force, it leads to significant mathematical difficulties. The current technique works on the operator, which is simple and effective when investigating fractal oscillators with external forces, easy to obtain analytic solutions, and doesn't lead to any mathematical difficulties

A fractionally time-delayed SD-Van der Pol oscillator with a non-perturbative approach

The primary target of the present article is to use a fast and efficient technique to obtain an analytical solution for a Duffing-Van der Pol-SD (D-VDP-SD) oscillator with a time delay. Depending on the smoothness parameter, this kind of vibration behaves in both discontinuous and smooth dynamical systems. This novel technique is presented for transmission from a nonlinear delay fractional oscillator to a linear classical oscillator with ordinary derivatives. The transformation into an equivalent oscillator is described in detail. Based on the comparison, the convergence of the numerical and analytical solutions appears satisfactory, which is an indicator of the accuracy of the solutions produced by the suggested technique

Solving Nonlinear Fractional Differential Equations for Contractive and Weakly Compatible Mappings in Neutrosophic Metric Spaces

In this article, we aim to prove various unique fixed point results for contractive and weakly compatible mappings in the sense of neutrosophic metric spaces. Several nontrivial examples are also imparted. To support main result, uniqueness of solution of nonlinear fractional differential equations is examined

Selective Extraction and Determination of Hydrocortisone and Dexamethasone in Skincare Cosmetics: Analytical Interpretation Using Statistical Physics Formalism

Molecularly imprinted polymers (MIPs), as magnetic extraction adsorbents, are used for the selective, rapid determination and extraction of dexamethasone and hydrocortisone in skincare products. Therefore, in this paper, magnetic molecularly imprinted polymers (MMIPs) and magnetic non-molecularly imprinted polymers (MNIPs) were utilized as adsorbents to describe the adsorption phenomena of dexamethasone and hydrocortisone. This interpretation, based on a statistical physics theory, applies the multilayer model with saturation to comprehend the adsorption of the drugs. Results obtained via numerical simulation revealed that dexamethasone and hydrocortisone adsorption happens via a non-parallel orientation on the surfaces of MMIPs and MNIPs, and they also showed that the adsorption amount of the MMIPs for the template molecule was notably greater than that of the MNIPs at the same initial concentration. The adsorption energy values retrieved from the data analysis ranged between 7.65 and 15.77 kJ/mol, indicating that the extraction and determination of dexamethasone and hydrocortisone is a physisorption process. Moreover, the distribution of a site’s energy was calculated to confirm the physical nature of the interactions between adsorbate/adsorbent and the heterogeneity of the surfaces of the MMIPs and MNIPs. Finally, the thermodynamic interpretation confirmed the exothermicity and spontaneous nature of the adsorption of these drugs on the tested adsorbents

An Efficient Analytical Method for Analyzing the Nonlinear Fractional Klein–Fock–Gordon Equations

The purpose of this article is to solve a nonlinear fractional Klein–Fock–Gordon equation that involves a recently created non-singular kernel fractional derivative by Caputo–Fabrizio. Motivated by some physical applications related to the fractional Klein–Fock–Gordon equation, we focus our study on this equation and some phenomena rated to it. The findings are crucial and essential for explaining a variety of physical processes. In order to find satisfactory approximations to the offered problems, this work takes into account a modern methodology and fractional operator in this context. We first take the Yang transform of the Caputo–Fabrizio fractional derivative and then implement it to solve fractional Klein–Fock–Gordon equations. We will consider three cases of the nonlinear fractional Klein–Fock–Gordon equation to ensure the applicability and effectiveness of the suggested technique. In order to determine an approximate solution to the fractional Klein–Fock–Gordon equation in the fast convergent series form, we can use the fractional homotopy perturbation transform approach. The numerical simulation is provided to demonstrate the effectiveness and dependability of the suggested method. Furthermore, several fractional orders will be used to describe the behavior of the given solutions. The results achieved demonstrate the high efficiency, ease of use, and applicability of this strategy for resolving other nonlinear issues

An Efficient Analytical Method for Analyzing the Nonlinear Fractional Klein–Fock–Gordon Equations

The purpose of this article is to solve a nonlinear fractional Klein–Fock–Gordon equation that involves a recently created non-singular kernel fractional derivative by Caputo–Fabrizio. Motivated by some physical applications related to the fractional Klein–Fock–Gordon equation, we focus our study on this equation and some phenomena rated to it. The findings are crucial and essential for explaining a variety of physical processes. In order to find satisfactory approximations to the offered problems, this work takes into account a modern methodology and fractional operator in this context. We first take the Yang transform of the Caputo–Fabrizio fractional derivative and then implement it to solve fractional Klein–Fock–Gordon equations. We will consider three cases of the nonlinear fractional Klein–Fock–Gordon equation to ensure the applicability and effectiveness of the suggested technique. In order to determine an approximate solution to the fractional Klein–Fock–Gordon equation in the fast convergent series form, we can use the fractional homotopy perturbation transform approach. The numerical simulation is provided to demonstrate the effectiveness and dependability of the suggested method. Furthermore, several fractional orders will be used to describe the behavior of the given solutions. The results achieved demonstrate the high efficiency, ease of use, and applicability of this strategy for resolving other nonlinear issues

On the feed-forward neural network for analyzing pantograph equations

Ordinary differential equations (ODEs) are fundamental tools for modeling and understanding a wide range of chemistry, physics, and biological phenomena. However, solving complex ODEs often presents significant challenges, necessitating advanced numerical approaches beyond traditional analytical techniques. Thus, a novel machine learning (ML)-based method for solving and analyzing ODEs is proposed in the current investigation. In this study, we utilize a feed-forward neural network (FNN) with five fully connected layers trained on data samples generated from the exact solutions of specific ODEs. To show the efficacy of our suggested method, we will conduct a thorough evaluation by comparing the anticipated solutions of the FNN with the exact solutions for some ODEs. Furthermore, we analyze the absolute error and present the loss functions for some ODE examples, providing valuable insights into the model’s performance and potential areas for further development

Mathematical Modeling and Analysis of the Steady Electro-Osmotic Flow of Two Immiscible Fluids: A Biomedical Application

The in vitro fabrication of big osteoarticular implants integrating biomaterials and cells is of tremendous interest because these tissues have a limited ability to regenerate. However, the growth of such cells in vitro is highly problematic, especially later in the culture, when the extracellular matrix has almost filled the initial porous network. Thus, the fluid flow required to properly perfuse the sample cannot be obtained by the hydraulic driving force alone. Fluid pumping is a central concern of a microfluidic system and electro-osmotic pumps (EOPs) are commonly employed for this purpose. Using electro-kinetic equations as a basis, this study analyzed the variations of a two-fluid electro-osmotic flow of viscoelastic fluid flow through a channel. The behavior of the fluid was studied through the Ellis equation. This is how the electro-osmotic pump functions, as demonstrated in the literature that it electrically drags a conducting fluid across a non-conducting fluid through interfacial dragging force along the channel. A steady-state analytical solution for the system in a conducting fluid channel was studied by undertaking an interface planner for fluids exhibiting Newtonian rheological properties. The pumping characteristics were studied in detail by using the Ellis model’s parameters. The fluid rheology was studied, which showed the viability of this technique

Examinations of mechanical, and shielding properties of CeO2 reinforced B2O3–ZnF2–Er2O3–ZnO glasses for gamma-ray shield and neutron applications

The glass system 75B2O3 - 4.5ZnF2 – 0.5 Er2O3–(20−x) ZnO- x CeO2, x = (0 ≤ x ≤ 1 mol. %) was manufactured using a melt quenching process, with CeO2 substituted for ZnO in the glass matrix in concentrations ranging from 0 to 1 mol %. The Makishima–Mackenzie model and sound wave velocity measurements were used to evaluate the mechanical parameters and elastic characteristics of the examined glass system, respectively. The results showed that increasing CeO2 doping ratio from 0 to 1 mol% increased density, sound velocities, elastic properties, and microhardness from 5.80 to 9.01 GPa. Phy-X/PSD software was employed to assess the effect of replacing ZnO with CeO2 on shielding capacity. The obtained results revealed that replacing ZnO with CeO2 enhances shielding characteristics and the manufactured glass may be useful in shielding applications