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This research delves into the propagation of radial free harmonic waves in a poroelastic cylinder, conceptualized as a magnetically and rotationaly influenced hollow structure. The primary aim is to elucidate the magnetic field's and rotation impact on the vibrational behavior of such systems. The investigative method encompasses the resolution of motion equations, formulated as partial differential equations, through the application of Lame's potential theory. This analytical process is augmented by the implementation of fitting boundary conditions, culminating in the derivation of a comprehensive expression for the complex dispersion equation, predicated on the premise that the wavenumber embodies a complex entity. The precision of the model is corroborated through a comparative analysis with established literature, underpinned by an exploration of diverse scenarios. The research employed MATLAB for both numerical and graphical assessments, focusing on the dispersion and displacement attributes. Dispersion relations within the poroelastic medium were computed, considering varied magnitudes of magnetic field intensity, rotation and angular velocities. The outcomes are articulated through complex-valued dispersion relations, transcendental formulations, and numerical resolutions employing MATLAB's bisection technique. These insights hold substantial significance for the theoretical advancement in orthopedic research, particularly concerning cylindrical poroelastic media. This study deduces that the radial vibrational patterns and the corresponding frequency equation within a poroelastic medium are profoundly modified by the magnetic field's interference and rotation. This study formulate a novel governing equation for a poroelastic medium, highlighting the significance of radial vibrations and investigating the impact of magnetic field and rotation.

Abstract In the study, we investigate the numerical investigation of variable viscous dissipation and source of heat or sink in mixed convective stagnation point flow the unsteady non-homogeneous nanofluid under the induced magnetic parameter. Considering similarity conversions, the governing of fundamental boundary of layer non-linear PDEs are transformed to equations of the non-linear differential type that, under appropriate boundary conditions, are numerically solved, and the MATLAB function bvp4c is considered to solve the resulting system. The obtained results are calculated numerically for non-dimensional velocity, temperature, and volume fraction and displayed graphically. Further, numbers of Nusselt and Sherwood and local Skin of friction have been produced and displayed by graphs. A comparison with previous results obtained neglecting the new parameters has been made to show the impact of new external parametes on the phenomneon. The obtained findings agree with those introduced by others if the magnetic field and viscous dissipation are neglected. The results obtained have an important applications in diverse field as chemical engineering, agriculture, medical science, and industries.

Since there is a clear correlation between poverty and corruption, mathematicians have been actively researching the concept of poverty and corruption in order to develop the optimal strategy of corruption control. This work aims to develop a mathematical model for the dynamics of poverty and corruption. First, we study and analyze the indicators of corruption and poverty rates by applying the linear model along with the Eviews program during the study period. Then, we present a prediction of poverty rates for 2023 and 2024 using the results of the standard problem-free model. Next, we formulate the model in the frame of Caputo fractional derivatives. Fundamental properties, including equilibrium points, basic reproduction number, and positive solutions of the considered model are obtained using nonlinear analysis. Sufficient conditions for the existence and uniqueness of solutions are studied via using fixed point theory. Numerical analysis is performed by using modified Euler method. Moreover, results about Ulam-Hyers stability are also presented. The aforementioned results are presented graphically. In addition, a comparison with real data and simulated results is also given. Finally, we conclude the work by providing a brief conclusion.

In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.

The mathematical model of the dynamics of HIV/AIDS infection transmission is developed by adding the set of infected but noninfectious persons, using a conformable fractional derivative in the Liouville–Caputo sense. Some fixed point theorems are applied to this model to investigate the existence and uniqueness of the solutions. It is determined what the system’s fundamental reproduction number R0 is. The disease-free equilibrium displays the model’s stability and the local stability around the equilibrium. The study also examined the effects of different biological features on the system through numerical simulations using the Adams–Moulton approach. Additionally, varied values of fractional orders are simulated numerically, demonstrating that the results generated by the conformable fractional derivative-based model are more physiologically plausible than integer-order derivatives.

In recent decades, because of the speedy progress of the smart grid and the deepening of the reforms of the energy system, demand-side users can contribute to the collaboration of the energy network, with the main right to public energy procurement and the main right to sell energy. The demand side of the smart grid and the open energy market provides users with more adoptions, and game theory is expected to become an important tool for optimizing multi-stakeholder decision-making and solving many problems in this area. In this regard, this review article first reviews the recent development of game theory application in modern power systems, in addition to discussing in detail the typical gaming behavior of the current energy demand side. Second, it focuses on the application of game theory mainly in three aspects: distributed energy users, high-energy energy users, and medium- and low-energy users. Game theory is used in optimizing the distributed energy coordination, optimizing the energy purchasing strategy, responding to the needs of commercial and residential users, and ensuring network communication. Later, a comprehensive analysis of recent trends in game theory application in power systems is carried out in detail.

Abstract In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

This article extracts stochastic soliton waves for the perturbed nonlinear Schödinger’s equation (PNLSE) forced by multiplicative noise through the Itô sense by utilizing two unified solver methods. The presented solutions involve three types: rational function, trigonometric function, and hyperbolic function solutions. These stochastic solutions are critical for studying numerous complicated phenomena in heat transfer, new physics, and many other fields of applied science. We demonstrate the effect of multiplicative noise on the solution of the stochastic PNLSE, which have never been studied before. The study and acquired solutions clarify that the unified solver technique is sturdy and efficient. Finally, several 2D and 3D graphs for selected solutions are shown.

In this paper, the three-phase-lag model of fractional analysis on the reflection of two-dimensional problem of p-waves with initial stress, temperature-dependent, and magnetic field is investigated. The formulation of the problem for an isotropic homogeneous medium based on a three phase-lag theory. The boundary conditions applied on the surface for the stresses and thermal insulation. The numerical solution presented as well as the graphical representation of the impact of analysis considering the external parameters. Also, the modified elastic waves reflected under the action of the magnetic field, initial stress, fractional degree coefficient, and temperature to determine the more exact nature of the reflection of these waves, particularly seismic waves. A comparison has been made between the results obtained and the previous results obtained by others and already published and are in agreement with these, when external parameters considered in the present investigation neglected. The results obtained indicate that the new external parameters have new impact on the waves reflection and applicable in diverse fields as engineering, earthquakes, volcanos, geophysics, acoustics, and astronomy.

In a current article, two novel analytical approaches are compared for analytical analysis of wave like equations with variable coefficients, which describe the evolution of stochastic phenomena. One is the New Approximate Analytical Method which based on Caputo–Riemann operator with simple decomposition procedure. This new method directly provides a fractional order series form solution which fastly converge to exact form solution for integer order. The second is Mohand Variational Iteration Transform Method which base on iteration procedure with Mohand Transform. The Mohand Variational Iteration Transform Method provides series form solution without using any decomposition, discretization, and He’s polynomial. The solution in series form converges directly to the exact solution for integer orders. The comparative analysis validates that Mohand Variational Iterative Method has less computational work and simple procedure without using any decomposition, discretization, and He’s polynomial procedure as compared to New Approximate Analytical Method.

We consider in this study the (3+1)-dimensional stochastic potential Yu–Toda–Sasa–Fukuyama with conformable derivative (SPYTSFE-CD) forced by white noise. For different kind of solutions of SPYTSFE-CD, including hyperbolic, rational, trigonometric and function, we use He’s semi-inverse and improved (G′/G)-expansion methods. Because it investigates solitons and nonlinear waves in dispersive media, plasma physics and fluid dynamics, the potential Yu–Toda–Sasa–Fukuyama theory may explain many intriguing scientific phenomena. We provide numerous 2D and 3D figures to address how the white noise destroys the pattern formation of the solutions and stabilizes the solutions of SPYTSFE-CD.

Several cells and microorganisms, such as bacteria and somatic, have many essential features, one of which can be modeled by the chemotaxis system, which we consider to be our main interest in this article. More precisely, we studied the hyperbolic system derived from the chemotaxis model with fractional dissipation, which is a generalization for the hyperbolic system with classical dissipation. The results of this article are divided into two parts. In the first part, we used energy methods to obtain the existence of small solutions in the Besov spaces. The second one deals with the optimal decay of perturbed solutions using a refined time-weighted energy combined with the Littlewood-Paley decomposition technique. To the authors’ best knowledge, this type of system (with fractional dissipation) has not been studied in the literature.

In this paper, we take into consideration the mathematical analysis of time-dependent quasistatic processes involving the contact between a solid body and an extremely rigid structure, referred to as a foundation. It is assumed that the constitutive law is fractional long-memory viscoelastic. The contact is considered to be bilateral and is modeled around Tresca’s law. We establish the existence of the generalized solution’s result. The proof is supported by the surjectivity of the multivalued maximum monotone operator, Rothe’s semidiscretization method, and arguments for evolutionary variational inequality.

The existence, uniqueness, and various forms of Ulam–Hyers (UH)-type stability results for nonlocal pantograph equations are developed and extended in this study within the frame of novel psi-piecewise Caputo fractional derivatives, which generalize the piecewise operators recently presented in the literature. The required results are proven using Banach’s contraction mapping and Krasnoselskii’s fixed-point theorem. Additionally, results pertaining to UH stability are obtained using traditional procedures of nonlinear functional analysis. Additionally, in light of our current findings, a more general challenge for the pantograph system is presented that includes problems similar to the one considered. We provide a pertinent example as an application to support the theoretical findings.