Neural networking study of worms in a wireless sensor model in the sense of fractal fractional

We are concerned with the analysis of the neural networks of worms in wireless sensor networks (WSN). The concerned process is considered in the form of a mathematical system in the context of fractal fractional differential operators. In addition, the Banach contraction technique is utilized to achieve the existence and unique outcomes of the given model. Further, the stability of the proposed model is analyzed through functional analysis and the Ulam-Hyers (UH) stability technique. In the last, a numerical scheme is established to check the dynamical behavior of the fractional fractal order WSN model

Solution of Singular Integral Equations via Riemann–Liouville Fractional Integrals

In this attempt, we introduce a new technique to solve main generalized Abel’s integral equations and generalized weakly singular Volterra integral equations analytically. This technique is based on the Adomian decomposition method, Laplace transform method, and Ψ-Riemann–Liouville fractional integrals. Finally, some examples are proposed and they illustrate the rapidness of our new technical method

Natural gas based on combined fuzzy TOPSIS technique and entropy

In the present study we have presented the notion of FUZZY BAYESIAN DECISION TECHNIQUE and combined the idea of the Fuzzy TOPSIS technique and entropy. We define the new ideas of fuzzy TOPSIS technique and entropy. So, we introduce the TOPSIS method and entropy, and the weights of the DMs are used. We proposed an MCDM technique based on TOPSIS and entropy. We focus on parameter different solutions of Fuzzy TOPSIS Positive ideal and Negative ideal solutions efficient decision making. Also, we provide a numerical example to elucidate the proposed technique stage by stage. Lastly, we compare the explanations of the current problem with the many existing MCGDM approaches to deliver the skills and rationality of the offered technique. We also provide a sensitivity study by shifting the entropy to establish the weights of the criteria underneath the dominant entropy measure meaning

Existence of results and computational analysis of a fractional order two strain epidemic model

In this paper, we investigate fractional order two strain epidemic model in the sense of ABC operator. This study includes existence and uniqueness of solution, stability and numerical simulations of the model under consideration. Fixed point postulates are used for the existence and uniqueness of solution. A theoretical approach is employed to investigate sufficient results for Hyers–Ulam’s stability to the model under study. For the numerical demonstration Lagrange’s interpolation polynomial technique is utilized. Graphical presentations against different fractional orders are displayed

Mathematical analysis of fractional order alcoholism model

In this manuscript, we are going to study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under the concept of conformable fractional order derivative (CFOD). Currently, most of real-world problems are considered under fractional order derivatives because of their stable and global behavior. First, we will investigate the model for qualitative theory including existence and uniqueness of solution and Ulam-Hyers stability. For qualitative theory, we will use fixed point theory. In addition, we use a numerical method to find the approximate solution of the proposed model. In the final part of the paper, we give a detailed discussion of its numerical results and its graphical presentation

Numerical Solutions of Variable Coefficient Higher-Order Partial Differential Equations Arising in Beam Models

In this work, an efficient and robust numerical scheme is proposed to solve the variable coefficients’ fourth-order partial differential equations (FOPDEs) that arise in Euler–Bernoulli beam models. When partial differential equations (PDEs) are of higher order and invoke variable coefficients, then the numerical solution is quite a tedious and challenging problem, which is our main concern in this paper. The current scheme is hybrid in nature in which the second-order finite difference is used for temporal discretization, while spatial derivatives and solutions are approximated via the Haar wavelet. Next, the integration and Haar matrices are used to convert partial differential equations (PDEs) to the system of linear equations, which can be handled easily. Besides this, we derive the theoretical result for stability via the Lax–Richtmyer criterion and verify it computationally. Moreover, we address the computational convergence rate, which is near order two. Several test problems are given to measure the accuracy of the suggested scheme. Computations validate that the present scheme works well for such problems. The calculated results are also compared with the earlier work and the exact solutions. The comparison shows that the outcomes are in good agreement with both the exact solutions and the available results in the literature

The Volterra-Lyapunov matrix theory and nonstandard finite difference scheme to study a dynamical system

A compartmental model is considered to study the transmission dynamics of COVID-19. The proposed model is investigated for different results by using Volterra-Lyapunov (V-L) matrix theory. In this regard, first we presented a modified form of SEIR model by incorporating three new compartments C (protected), D (death due to corona) and Q (quarantined). Both equilibrium points are computed together with basic reproductive number. In addition, local stability of both equilibrium points for our proposed model is examined by assuming that wearing of mask, testing of the unaware infected individuals and medical care of the individuals that got infected should constantly be maintained. Hence, subsequently by combining the V-L stable matrix theory with the traditional methodology of constructing the Lyapunov functions, a procedure for the global stability analysis of COVID-19 is presented. Furthermore, based on LaSalle and Lipschitz invariance principle, the global stability of disease free equilibrium point is also examined. The technique we introduced in this paper will provide the more profound comprehension to understand the basic structure of COVID-19. Moreover, for numerical interpretation of our proposed model non-standard finite difference (NSFD) scheme is utilized for simulations. Different graphical illustrations are provided to understand the transmission dynamics

Effect of Weather on the Spread of COVID-19 Using Eigenspace Decomposition

Since the end of 2019, the world has suffered from a pandemic of the disease called COVID-19. WHO reports show approximately 113 M confirmed cases of infection and 2.5 M deaths. All nations are affected by this nightmare that continues to spread. Widespread fear of this pandemic arose not only from the speed of its transmission: a rapidly changing "normal life" became a fear for everyone. Studies have mainly focused on the spread of the virus, which showed a relative decrease in high temperature, low humidity, and other environmental conditions. Therefore, this study targets the effect of weather in considering the spread of the novel coronavirus SARS-CoV-2 for some confirmed cases in Iraq. The eigenspace decomposition technique was used to analyze the effect of weather conditions on the spread of the disease. Our theoretical findings showed that the average number of confirmed COVID-19 cases has cyclic trends related to temperature, humidity, wind speed, and pressure. We supposed that the dynamic spread of COVID-19 exists at a temperature of 130 F. The minimum transmission is at 120 F, while steady behavior occurs at 160 F. On the other hand, during the spread of COVID-19, an increase in the rate of infection was seen at 125% humidity, where the minimum spread was achieved at 200%. Furthermore, wind speed showed the most significant effect on the spread of the virus. The spread decreases with a wind speed of 45 KPH, while an increase in the infectious spread appears at 50 KPH