Generalized Hukuhara Conformable Fractional Derivative and its Application to Fuzzy Fractional Partial DifferentialEquations

The main focus of this paper is to develop an efficient analytical method to obtain the traveling wave fuzzy solution for the fuzzy generalized Hukuhara conformable fractional equations by considering the type of generalized Hukuhara conformable fractional differentiability of the solution. To achieve this, the fuzzy conformable fractional derivative based on the generalized Hukuhara differentiability is defined, and several properties are brought on the topic, such as switching points and the fuzzy chain rule. After that, a new analytical method is applied to find the exact solutions for two famous mathematical equations: the fuzzy fractional Wave equation and the fuzzy fractional Diffusion equation. The present work is the first report in which the fuzzy traveling wave method is used to design an analytical method to solve these fuzzy problems. The final examples are asserted that our new method is applicable and efficient.

Exact analytical solution of the influence of an external centrifugal field and the heat transfer on a confined gas between two plates in the unsteady state

This paper aims to study the non-stationary situation of the effectiveness of an external centrifugal force (ECF) and the heat transfer (HT) on the manner of neutral gas (NG). We solve a system of non-linear non-stationary partial differential equations, which represents an enormous task. Our model is examined to follow the manner of the macroscopic properties of the NG that bounded between two parallel horizontal rigid fixed plane plates (HRFPPs). The moment method and the traveling wave method are utilized. The draw an analogy among the perturbed distribution function (DF), and the equilibrium DF with time is studied. The thermodynamic predictions are calculated. System internal energy change (IEC) is investigated. We applied the results for laboratory helium NG. We detected that in specific conditions, we could compensate for the decreasing of particles’ number adjacent to the lower HRFPP because of the centrifugation process, with other particles adjacent to the higher heated HRFPP. We did that with the help of the reverse heat current from the heated upper HRFPP, which gave us a considerable enhancement and development of gases isotope separation processes. Furthermore, we approved that our model is compatible with the second law of thermodynamics, the rule of Le Chatelier, and the H-Theorem of Boltzmann. Those investigations were done with a non-restricted range of the temperatures ratio factor, the centrifugal Mach number, and the Knudsen numbers. The significance of this study was due to its vast applications in numerous fields, such as in physics, engineering, biomedical, and various commercial and industrial applications.

Accurate Location of Faults in Transmission Lines by Compensating for the Electrical Distance

Accurately locating faults is quite important, especially when the geographical environment is complicated. If the exact location of the fault is not given, wrong route would be chosen, which will greatly slow down repair. This paper proposes an improved traveling wave method by compensating the electrical distance of transmission lines. The catenary model is constructed that considers parameters of the tower and the actual temperature. The actual line length is also derived by the catenary model. A 500 kV transmission line model is established by PSCAD/EMTDC. Various fault simulations are conducted and the results demonstrate that the presented method effectively reduces the error ratio of faulty segment positioning and locates faults with high accuracy.

ИССЛЕДОВАНИЕ СЕЙСМОСТОЙКОСТИ ГРУНТОВЫХ ПЛОТИН ОТ ДЕЙСТВИЯ МНОГОКРАТНЫХ СЕЙСМИЧЕСКИХ ВОЗДЕЙСТВИЙ, СООРУЖЕННЫХ В ГОРНО- СКЛАДЧАТЫХ РЕГИОНАХ

The problem of seismic stability of homogeneous earth dams constructed in complex geohydrodynamic regions has been solved. The calculations are performed using from the finite element method. Given the great extent at the base of such dams, the general equation of their motion is solved taking into account the well-known “traveling wave” method. It is shown that the offset of the existing viscous-plastic properties of earth dams already under the influence of a one-time strong seismic impact in them residual deformations arise, which subsequently develops even with weak earthquakes. This circumstance must be taken into account when designing such dams.