Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance

Resonances of a fractional-order biomedical model with time delay state feedback

In the present paper, the primary resonance of a fractional-order Willis aneurysm system with time-delay state feedback control is studied. Using the multiple scale method, the amplitude and phase equations are obtained. The first order approximate solution is derived and the influence of time delay on resonance is studied. The concept of equivalent damping related to time-delay feedback is proposed, and the reasonable selection of feedback gain and time delay is discussed from the point of view of vibration control. The frequency response and external excitation response curves of the system are given. In order to test the stability of the system, bifurcation analysis is carried out. The obtained results are very useful in the clinical diagnosis and treatment of cerebral aneurysms

Empirical Study on the Sustainability of China’s Grain Quality Improvement: The Role of Transportation, Labor, and Agricultural Machinery

As a major part of farming sustainability, the issues of grain production and its quality improvement have been important in many countries. This paper aims to address these issues in China. Based on the data from the main production provinces and by applying the stochastic frontier analysis methodology, we find that the improvement of transportation and the use of agricultural machinery have become the main driving forces for grain quality improvement in China. After further studying different provinces’ potentials of grain quality improvement, we show that grain quality has increased steadily. Therefore, we can conclude China’s grain quality improvement is indeed sustainable. Furthermore, different grains like rice, wheat, and corn share similar characteristics in terms of quality improvement, but the improvement rate for rice is relatively low, while those of corn and wheat are relatively high. Moreover, the overall change of efficiency gain of grain quality improvement is not significant for different provinces. The efficiency gains of the quality improvements for rice and wheat even decrease slightly. In addition, we find that only expanding grain quality improvement potential can simultaneously achieve the dual objectives of improving grain quality and increasing yield

Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance

Measuring Social Vulnerability to Flood Disasters in China

To proactively prevent losses from flood disasters and subsequent potential human conflicts, it is critical to measure the social vulnerability of a country or a region to flood. In this article, we first propose a list of potential indicators for measuring this social vulnerability. These indicators’ significances are then tested based on their correlation coefficients with a vulnerability index obtained using nonparametric Data Envelopment Analysis. In the final measurement system, there are nine indicators: the proportion of the primary industry, infrastructure development level, income gap between urban and rural residents, the proportion of population over 60 years old, the proportion of children under 14 years old, the number of people receiving minimum income assistance, and the number of disasters per year. We then conduct principal component analysis to evaluate the social vulnerability level. Our results show that the social vulnerability level is mostly impacted by the economic principal component and the demographic and social security principal component. Moreover, our results also confirm that the social vulnerability level to flood in China declined overall from 2003 to 2015

Existence Results for a Class of the Quasilinear Elliptic Equations with the Logarithmic Nonlinearity

In this paper, the nonlinear quasilinear elliptic problem with the logarithmic nonlinearity −div∇up−2∇u=axφpulogu+hxψpu in Ω⊂Rn was studied. By means of a double perturbation argument and Nehari manifold, the authors obtain the existence results