Chaos, Solitons and Fractals: X最新文献

A Hadamard fractional boundary value problem with semi-positone nonlinearity is studied in this paper, and the local existence and uniqueness of solutions are derived by a recent fixed point theorem involving with increasing $\phi -(h,r)$-concave operators defined on ordered spaces. This is an unprecedented approach to solve the semi-positone problems. In practice, this method has a wider range of applicability since it can obtain the local uniqueness of the solutions. Furthermore, we can approximate the unique solution by constructing convergent iterative sequences. In the end, a persuasive example is provided to illustrate that the theoretical results we obtained are applicable and valid.

We analyze a peakon - antipeakon collision for essentially non-integrable versions of the Camassa-Holm equation. Using the matching and weak asymptotics methods, we construct an asymptotic solution that satisfies both a one-parameter family of equations (with a parameter r), and two energy laws. It is shown that the original waves with amplitudes $A_1>0$ and $A_2<0$ are reflected upon collision and form new waves with amplitudes $B_1<0$ and $B_2>0$ such that, depending on the parameter r, either $B_1=A_2$ and $B_2=A_1$, or $B_i$ are arbitrary numbers provided $B_1+B_2=A_1+A_2$.

In this study, an analysis of the perturbation factors and fractional order derivatives is performed for the novel singular model. The design of the perturbed fractional order singular model is presented by using the traditional form of the Lane-Emden along with the detail of singular points, fractional order, shape, and perturbed factors. The analysis of the perturbation factors and fractional order terms for the singular model is provided in two steps by taking three different values of the perturbed term as well as fractional order derivatives. The numerical analysis of the perturbation and fractional order terms for the novel fractional Meyer wavelet neural network (FMWNN) along with the global and local search effectiveness of the genetic algorithm (GA) and active-set algorithm (ASA) called as FMWNN-GAASA. The modeling of the FMWNN is presented in terms of mean square error, while the optimization is performed through the GAASA. The authentication, validation, excellence, and correctness of the singular model are observed by using the comparative performances of the obtained and the reference solutions. The stability of the proposed stochastic scheme is observed through the statistical performances for taking large datasets to present the analysis of the perturbation and fractional order terms.

Public goods games between model agents with bounded rationality and a simple learning rule, which have been previously shown to represent experimentally observed human playing behavior, are studied by direct simulation on various lattices with different network topology. Despite strong coupling between playing groups, we find that average investments do not significantly depend upon network topology, but are determined solely by immediate local network environment. Furthermore, the dependence of investments on characteristic agent parameters factorizes into a function of individual cognitive budget, K, and a simple function $1/(1+c(0)/\beta )$, where $c\left(0\right)$ is the group centrality and $\beta =12.5$ for all networks investigated. Given the good agreement of agent behavior with available experiments, this seems to indicate that even complex societal networks of investment in public goods may be accessible to predictive simulation with limited effort.

Dengue is a significant factor to the global public health issue, including Nepal. In Nepal from $2004-2022$, the largest outbreak occurred in the year 2022. Dengue infection cases appeared all over 77 districts of Nepal. The Caputo fractional order SEIR-SEI epidemic model is able to describe dengue disease transmission dynamics of present situation. For fundamental mathematical guarantees of epidemic model equations, we studied the Lipschitz and Banach contraction theorems to show that the model equations have a unique solution. The Ulam-Hyres stability is established in the model. Next generation matrix approach is used to calculate the associated basic reproduction number $R_0$. The model equilibrium points are identified, and the local asymptotic stability for disease-free equilibrium point is analyzed. Normalized forward and partial rank correlation coefficient are used for sensitivity study to identify the factors that affect dengue infection with respect to basic reproduction number. Using real data of Nepal, the model is fitted and the least square method is used for estimating parameters. Numerical scheme has been illustrated using a two-step Lagrange interpolation approach and the solution is approximated. With numerical results and sensitivity analysis, it is concluded that biting rate and death rate of mosquito are extremely sensitive to the disease transmission. The transmission increases with increasing biting rate and decreases with decreasing mosquito death rate. For the year 2022, $R_0=1.7739>1$ showing that the disease is endemic. Thus, effective control measure should be implemented to combat the dengue virus. However, further research needs to be undertaken to assess the impact of such control measures.

In the current work, we examine $\eta$-Ricci-Yamabe solitons in a Bochner flat Lorentzian K$\ddot{a}$hler space-time manifolds. We have addressed various circumstances for Ricci-Yamabe solitons to be steady, shrinking or expanding in terms of isotropic pressure, the cosmological constant, energy density and gravitational constant in different perfect fluids such as dark fluid, Stiff matter, dust fluid and radiation fluid.

We consider a novel approach to providing highly accurate analytic solutions to non-classical, non-linear problems. This approach is then implemented to the highly sensitive Troesch-problem, which possesses a boundary layer at the right-end: we determine an upper and lower envelope solution, and compare the average to existing numerical results. Computer simulations show that the proposed analytic solution is highly accurate when compared to the existing benchmark. This confirms that the proposed approach to deal with such non-linear problems can be used to treat similar non-classical boundary-value problems.

COVID-19 pandemic affects 213 countries and regions around the world. Which the number of people infected with the virus exceeded 26 millions infected and more than 870 thousand deaths until september 04, 2020, in the world, and Peru among the countries most affected by this pandemic. So we proposed a mathematical model describes the dynamics of spread of the COVID-19 pandemic in Peru. The optimal control strategy based on the model is proposed, and several reasonable and suitable control strategies are suggested to the prevention and reduce the spread COVID-19 virus, by conducting awareness campaigns and quarantine with treatment. coronavirus 2019 (COVID-19). Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab.

Stochastic fractional integrodifferential models are widely employed to model several natural phenomena these days. This current work focuses on the well-posedness results and numerical solutions of a specific form of these models considering the Leffler nonsingular kernels operator wherein the stochastic term is driven by the standard Brownian motion. Accordingly, a combination of sufficient conditions, topological theorems, and Banach space theory are utilized to construct the well-posedness proof. For treating the numerical issue, a familiar spectral collocation technique relying upon shifted Legendre series expansion theory is proposed. The basic properties of Brownian motion and a linear spline interpolation method are used to simulate the standard Brownian motion at a fixed time value. In addition, the idea of the Gauss-Legendre numerical integration rule is implemented to approximate the finite integral. We also devote our attention to the concept of convergence of the proposed method and demonstrate its analysis. Ultimately, the obtained theoretical results and the presented method are examined with five numerous applications. The obtained results indicate the high accuracy and efficiency of applying this method in solving stochastic models of the above-mentioned form.

As an important research direction of swarm intelligence algorithm, particle swarm optimization (PSO) has become a popular evolutionary method and received extensive attention in the past decades. Despite many PSO variants have been proposed, how to maintain a good balance between the exploration and exploitation abilities, and how to jump out of the local optimal position are still challenges. In this article, based on empirical balance strategy, a new particle swarm optimization (EBPSO) algorithm is presented. Firstly, based on an adaptive adjustment mechanism, the algorithm can choose a better strategy from two search equations, which can maintain the balance between the exploration and exploitation abilities. Secondly, to utilize the information of individual historical optimal solution and the optimal solution of the current population, a weight for adjusting their influence is introduced into the search equation. Thirdly, by introducing the diversity of population, a moving equation for dynamically adjusting the search ability of the algorithm is proposed. Finally, to avoid falling into local optimum and to search the potential location, a dynamic random search mechanism is proposed, which is designed by using the information of the current optimal solution. Compared with some state-of-the-art algorithms, the experimental results show that EBPSO has excellent solution quality and convergence characteristic on almost all test problems.