Nonlinear Differential Systems Research Articles

Effects of radiation and activation energy on magnetized ternary nanofluid flow produced by a slippery elastic sheet with entropy analysis

This study looks into two-dimensional, incompressible magnetohydrodynamic flow of ternary hybrid nanofluid passing a stretched surface through a porous material taking into consideration activation energy, heat sink, chemical reaction parameter, and viscous dissipation. This study’s aim is to analyse the flow behaviour for temperature, concentration and velocity with entropy in the presence of titanium dioxide, aluminium oxide, and copper oxide nanoparticles. An effective similarity conversion procedure is used to transform partial differential equations to a nonlinear ordinary differential equations system. Employing proper boundary restrictions, the nonlinear equations are solved using the MATLAB bvp4c technique. A number of physical flow parameters including velocity, thermal and concentration profiles are investigated through tables and graphs in order to assess the flow behaviour. The main outcomes indicate that the velocity profile was decreased by the magnetic parameter and porosity parameter. Also, the Brinkmann number rises the entropy generation rate, while radiation and Brinkmann number decrease the Bejan number. The Sherwood number falls with larger activation energy and magnetic parameter, while it improves with increased Schmidt number, radiation parameter and chemical reaction parameter.

Analytical simulation of Darcy–Forchheimer nanofluid flow over a curved expanding permeable surface

Abstract This research paper presents an analytical simulation of Darcy–Forchheimer flow over a porous curve stretching surface. In fluid dynamics, the Darcy–Forchheimer model combines Forchheimer adjustment and high-velocity effects with Darcy’s formula for porous media flow: two nanofluid particles, molybdenum disulphide, and graphene oxide, form nanofluid with the base fluid blood. The governing partial differential equations for momentum and energy are converted into a nonlinear ordinary differential equations system by applying the appropriate similarity transformations. The homotopy analysis method is used to solve the transform equations analytically. The impact of essential factors includes the Forchheimer parameter, porosity parameter, slip parameter, Eckert number, nanoparticle volume friction, magnetic field parameter, and curvature parameter. The results have applications in the design of sophisticated cooling systems, where effective thermal control is essential.

Global Stability of Fractional Nonlinear Differential Systems With State-Dependent Delayed Impulses.

The fractional-order (FO) nonlinear differential system with state-dependent (SD) delayed impulses (DI) is considered in this brief. The considered impulses are related to the delayed state of the system and the delays are SD. A novel lemma for the monotonicity of the solution of Caputo's FO derivative equation is given. By means of linear matrix inequality (LMI) and several comparative arguments, criteria of uniform stability, uniform asymptotical stability, and Mittag-Leffler stability are obtained. Compared with other works on integer-order (IO) impulsive delayed systems with SD delays or fixed delays, how to impose constraints on parameters and impulses is explored, without imposing the boundedness on the state delays. Two examples are implemented to examine the practicality and sharpness of our theoretical analysis.

Drone Delivery Trajectory Prediction Using Nonlinear First-order Systems and Their Numerical Solutions

Abstract Drone delivery trajectory prediction under extreme weather condition is an essential issue to consider in the application of unmanned aerial vehicles. In this paper, the nonlinear first-order differential equation system is established to describe the drone delivery trajectory, where the wind is considered in different formulations. In autonomous case where the variable “time” does not involve in equation system, the analytical solution is obtained. In the non-autonomous cases where variable “time” appear in our system, the numerical solutions are achieved by using the fourth-order method of Runge-Kutta. From the graphs of these solutions, it is clear to see that the nonlinear first-order systems proposed in this paper are reasonable to predict the trajectory of the unmanned aerial vehicle under different wind scenarios.

Analytical Modeling of Mass and Heat Transfer on Unsteady Squeezing Viscous Nanofluid Flow under the Influence of Slip Velocity

In this article, two-dimensional unsteady incompressible viscous nanofluids magneto-hydrodynamic (MHD) flow among two parallel plates extended infinitely is investigated. The equations that results from the use of similarity transformations for non-linear partial differential system are solved by the new algorithm. The important key to this construct is the derivatives that appear as coefficients in the power series. The effects of apparent physical parameters on velocity concentration and temperature distributions are described using a schematic diagram and interpreted physically. The effects of apparent physical parameters on concentration, temperature, and velocity distributions are described by graphs. For the flow of nanofluids, the results indicate that it is inversely proportional between the rate of mass and heat transfer with nanoparticle size fraction and magnetic parameter. Over time, squeeze number and schmidt number lead to increase the rate of mass transfer. This problem is dissolved numerically by using the Runge-Kutta scheme of fourth-order (RK4S) .

Application of fibonacci wavelet frame operational matrix for the analysis of arrhenius-controlled heat transfer flow in a microchannel

The effects of free convective Arrhenius-controlled heat transfer fluid in a microchannel encased by two parallel vertical plates has been examined in the current work. A new functional integration matrix has been developed by implementing Fibonacci Wavelet Frame known as Fibonacci wavelet Frame operational matrix. Primary goal of this study is to provide a unified method via FWF to compute an approximate solution to a non-linear differential equation systems for the fluid flowing in a microchannel. The leading nonlinear coupled differential equations has been tackled by this novel approach. The derived results are discussed visually and displayed with the help of various plots. Additionally, thermophysical parameters of engineering interest, such as the nusselt number and sheer stress are estimated and depicted in the graphs. It is worthwhile to note that fluid velocity and fluid temperature rises as the chemical reaction parameter value enhances. A remarkable agreement comes to light when the numerical data generated through the current method is compared with the findings from the previous work.

Significance of gyrotactic microorganism's analysis for magnetized convectively heat 3D Sisko fluid flow with bioconvection phenomenon

In this research article, the bioconvection of oxytactic microorganisms with magneto-hydrodynamic (MHD) 3D steady flow of Sisko nanomaterial over a stretching sheet through convective conditions is deliberated and analyzed. Possessions of thermophoresis, Brownian motion as well as mixed convection in the Sisko fluid are also deliberated. Sisko fluid is supposed to be electrically conducted over and done with a constant pragmatic magnetic field. The flow problem is communicated using governing relations and problem is transmuted into dimensionless form among non-similar procedure. To obtain convergent solutions we must solve nonlinear differential systems. The consequences of several physical parameters have been deliberate and discussed. Our results displayed that the higher microorganism difference parameter condensed the microorganism profile, while an opposite influence is established for magnetic parameter. Concentration proises of the Sisko fluid flow are improved by growing Biot number whereas contracted beside the Lewis number. In recent years, the scientists have shown great attention in the field of bioconvection owing to its countless applications such as amassing the cells, bioreactors, gas-bearing sedimentary, modeling oil, exclusion of living, and nonliving cells, and lots of additional.

On a class of generalized capillarity system involving fractional ψ$$ \psi $$‐Hilfer derivative with p(·)$$ p\left(\cdotp \right) $$‐Laplacian operator

This research delves into a comprehensive investigation of a class of ‐Hilfer generalized fractional nonlinear differential system originated from a capillarity phenomena with Dirichlet boundary conditions, focusing on issues of existence and multiplicity of nonnegative solutions. The nonlinearity of the problem, in general, does not satisfy the Ambrosetti–Rabinowitz type condition. We use minimization arguments of Nehari manifold together with variational approach to show the existence and multiplicity of positive solutions of our problem with respect to the parameter in appropriate fractional ‐Hilfer spaces. Our main result is novel, and its investigation will enhance the scope of the literature on coupled systems of fractional ‐Hilfer generalized capillary phenomena.

Existence of positive solutions to impulsive nonlinear differential systems of second order with two point boundary conditions

Existence of positive solutions to impulsive nonlinear differential systems of second order with two point boundary conditions

Neural network optimal control for tripartite UAV confrontation systems based on fuzzy differential game

The neural network optimal control strategy based on a fuzzy differential game is proposed for the tripartite UAV confrontation systems consisting of the attackers, defenders, and targets. Firstly, the tripartite UAV mutual confrontation model is constructed and a nonlinear differential control system is established. Secondly, combining the fuzzy evaluation method and differential game theory, the tripartite UAV are divided into two parts of the confrontation game: attackers-defenders and attackers-targets. The optimal control strategies for the attackers, defenders and targets parties are derived separately. Then, the tripartite UAV game model is considered to be difficult to solve directly. The evaluation neural network is introduced to approximate the optimal value function using an adaptive dynamic programming method. The convergence of the evaluation neural network weights and the stability of the nonlinear differential control system are proved by using Lyapunov stability theory. Finally, the effectiveness of the tripartite UAV confrontation game control strategy designed in this paper is verified by simulation.

Stability analysis of dual solutions for nonlinear radiative magnetohydrodynamic flow of [formula omitted] hybrid nanofluid over a nonlinearly shrinking surface

The present work explores the existence and temporal stability of dual solutions with the consequence of nonlinear thermal radiation on hybrid nanofluid flow (including Silver and Titanium dioxide nanoparticles in water) past a permeable shrinking sheet. The analysis also considers the united outcomes of suction/injection, Joule heating, viscous dissipation, and magnetohydrodynamics. Employing realistic assumptions and suitable similarity transformations, the governing nonlinear partial differential equations are formulated and altered into a nonlinear ordinary differential equations system. These equations are then solved numerically using the Lobatto IIIA technique. It is observed that dual solutions can occur within a precise range of the shrinking surface parameter. Analyzing the temporal stability of these dual solutions under small disturbances shows that the upper solution branch is stable and represents a physically realistic solution to the problem. In contrast, the lower solution branch is unstable and not physically realizable. No solution exists beyond the critical λc=−1.3915 for the shrinking parameter. The critical values of shrinking parameter λc=−1.2565,−1.3188, and −1.4161 correspond to volume fractions of hybrid nanofluid with φAg−TiO2 of 2%,4%, and 8%, respectively. No solution exists beyond this critical point. The graphical representation and quantitative explanation demonstrate how various emergent characteristics affect momentum and thermal boundary layer profiles, Nusselt number, and skin friction. The velocity and temperature profile of hybrid nanofluid can be improved by adding a small volume of nanoparticle volume fraction. Thermal boundary layer thickness is amplified by an accumulation in the shrinking parameter, power index of velocity component, thermal radiation parameter, and temperature difference ratio. Sheering stress and heat transfer coefficient improve with adding more nanoparticles in the base fluid for the first solution braches, but opposite effects are found in the second solutions. The contributions of this research are significant both theoretically, in terms of advancing the mathematical modeling of hybrid nanofluid flow with heat transfer in engineering systems, and practically, in terms of applications to engineering cooling systems.

New exploration on approximate controllability of nondensely defined Hilfer neutral-type delayed nonlinear differential inclusion system with non-instantaneous impulse

This manuscript aims to investigate the existence and approximate controllability results for integral solution of nondensely defined Hilfer neutral differential inclusion system of Sobolev-type with infinite delay and non-instantaneous impulse in a Hilbert space. By utilizing the semigroup theory of bounded linear operators, fixed point technique, fractional calculus, and the theory of multivalued maps, the principal discussions are demonstrated. The sufficient conditions for the existence and approximate controllability are demonstrated under the consideration that the linear operator A is defined nondensely and satisfies the Hille–Yosida condition. Finally, an example is given to support the validity of the study.

Design of Nonlinear Delay Differential System for Analyzing Vulnerabilities in Nanoscale Hardware Implants: A Deep Dive into Intelligent Computing Networks

Design of Nonlinear Delay Differential System for Analyzing Vulnerabilities in Nanoscale Hardware Implants: A Deep Dive into Intelligent Computing Networks

A COMPUTATIONAL AND FRACTIONAL MATHEMATICAL MODEL FOR ASSESSING HEPATITIS B WITH OPTIMAL THERAPY

This paper presents a mathematical study applied to Hepatitis B disease utilizing fractional calculus and numerical methods. We begin by discussing mathematical fundamentals, focusing on fractional calculus concepts and relevant numerical aspects for disease modeling. We then formulate the problem, describing a nonlinear fractional differential system that models hepatitis B virus (HBV) infection and its response to drug therapy. A detailed theoretical analysis explores system properties and biological implications. We provide a qualitative analysis of the model, discussing important dynamic behaviors such as stability and parameter sensitivity. Subsequently, numerical analysis is performed to validate the model and estimate unknown parameters from patient data. Our findings include significant insights into biological parameters and their impact on therapeutic response. We conclude that the proposed fractional-order model is effective, offering optimal therapeutic strategies for hepatitis B.

Stability Analysis of a Class of Nonlinear Fractional Differential Systems With Riemann-Liouville Derivative

This paper investigates the stability of n-dimensional nonlinear fractional differential systems with Riemann-Liouville derivative. By using the Mittag-Leffler function, Laplace transform and the Gronwall-Bellman lemma, one sufficient condition is attained for the asymptotical stability of a class of nonlinear fractional differential systems whose order lies in (0, 2). According to this theory, if the nonlinear term satisfies some conditions, then the stability condition for nonlinear fractional differential systems is the same as the ones for corresponding linear systems. Several examples are provided to illustrate the applications of our result.

Impact of multiple slips and thermal radiation on heat and mass transfer in MHD Maxwell hybrid nanofluid flow over porous stretching sheet

This study investigates the two-dimensional magnetohydrodynamic (MHD) boundary-layer flow over a stretching sheet embedded in a porous medium, focusing on the innovative use of hybrid nanofluids. The research has practical applications in heat exchangers, nanofluid technology, porous media, and MHD systems. Key governing parameters, including internal heat sources/sinks, multiple slips, and thermal radiation, are analyzed for their impact on the flow. The nanofluid consists of hybridized nanoparticles (Alumina-Magnetite) dispersed in a water and ethylene glycol mixture (WEG-50:50). Assuming steady-state, incompressible, and laminar flow with small boundary layer thickness and constant nanofluid properties, the governing equations for continuity, momentum, energy, and species concentration are formulated. The fluid is modeled as a non-Newtonian (Maxwell) fluid. The resulting nonlinear ordinary differential equations system, with specified boundary conditions, is solved using the Runge-Kutta integration scheme implemented in MAPLE 23. Numerical results of heat transfer rates are validated against existing data, showing a 12 % increase in the Nusselt number for the WEG-Al2O3 nanofluid and a 20 % increase for the hybrid WEG- Al2O3–Fe3O4 nanofluid. It is demonstrated that skin friction decreases by up to 15 % with increased thermal Grashof number and that the Nusselt number can be reduced by up to 10 % due to magnetic effects. Overall, hybrid nanofluids generally demonstrate higher Nusselt and Sherwood numbers, enhancing heat transfer efficiency.

Neural networks-based framework for recognizing streaming patterns in magnetized Maxwell–Oldroyd-B blood blended with tetra-hybrid nanoparticles and microbes over stenosis in an elastic artery

The proposed study delves into investigating blood flow patterns and thermal and solutal transport in an artery affected by stenosis. Specifically, it explores the behavior of blood ingrained with tetra-hybrid nanoparticles and gyrotactic microbes under magnetic effects. To capture the non-Newtonian nature of blood in such complex scenarios, the Maxwell-Oldroyd-B (MO) fluid model is employed. The pertinent nonlinear partial differential equations system accounts for similarity transformations and boundary layer assertions. Numerical results are assessed using a potent shooting approach with a fourth-order Runge–Kutta (RK4) method implemented through MATLAB’s bvp4c commands. The computational outcomes are visualized via graphical representation and tabulated data for in-depth analysis and illustration. The research yields significant insights into various model parameters. For instance, the Lorentz force is observed to exert a drag effect, hindering blood flow velocity, while the opposite trend is observed for blood temperature. Additionally, higher Peclet numbers correlate with reduced mass concentration levels, while gyrotactic microbes’ density profile exhibits an upsurge with elevated Lewis numbers. Notably, the Nusselt number for Newtonian blood is lower than MO blood, shedding light on the impact of blood properties on heat transport. Furthermore, this study proposes a technique based on artificial neural networks (ANNs) for accurately predicting skin friction coefficient, Nusselt number, Sherwood number, and microbes’ density number. The proposed algorithm achieves remarkable accuracy rates of 99.65% on the testing dataset and 99.99% during cross-validation for predicting the skin friction coefficient. The novel findings generated by this model hold promising implications for the treatment and monitoring of arterial diseases, as well as the development of cutting-edge medical devices and technologies.

New global exponential stability conditions for nonlinear delayed differential systems with three kinds of time-varying delays

For a class of nonlinear differential systems with heterogeneous time-varying delays, including distributed, leakage and transmission time-varying delays, a novel global exponential stability (GES) analysis method was developed. Based on the GES definition, some sufficient conditions and rigorous convergence analysis of nonlinear delayed differential systems are presented directly, which ensure all states to be globally exponentially convergent. The proposed analysis method not only avoids the construction of the Lyapunov–Krasovskii functional, but also uses some simple integral reduction techniques to determine the global exponential convergence rate. Furthermore, the main advantages and low calculation complexity are demonstrated through a theoretical comparison. Finally, three numerical examples are provided to verify the effectiveness of the theoretical results.

Interval observer design for unobservable switched nonlinear partial differential equation systems and its application

SummaryThis paper designs an interval observer for switched nonlinear partial differential equation (PDE) systems. Initially, persistent dwell‐time switching rules are used to model switched PDE systems with fast and slow switching phenomena. Next, for unobservable systems caused by uncertainties, the interval observer for the target PDE systems is proposed by utilizing unknown but bounded information of the initial states, boundary conditions, external disturbances, and measurement noises. Subsequently, by utilizing the estimated state's upper and lower bounds, an interval observer‐based control strategy is devised to stabilize the studied systems, and sufficient conditions to ensure the stability of the target systems and the observation error dynamics are provided. Furthermore, the designed interval observer is employed to detect sensor failures in the presence of various uncertainties. Finally, two examples, including the lithium‐ion battery's temperature estimation and fault detection, are utilized to demonstrate the effectiveness of the obtained methods.

Numerical and analytical approach of nonlinear fractional pantograph nonlocal differential systems with non-singular kernel

Numerical and analytical approach of nonlinear fractional pantograph nonlocal differential systems with non-singular kernel