Solution of Multi-order Fractional Differential Equation Based on Conformable Derivative by Shifted Legendre Polynomial

The aim of this article is the way for finding approximation solution of multi-order fractional differential equation with conformable sense with use approximated function by shifted Legendre polynomial, the method is easy and powerful for get our results of the linear and non-linear equation, the background idea behind this method is finding system of algebra after achieving messing variable is that mean obtain approximate solution, a few examples illustrates for presented how much our method is capable.

Non-linear equation for estimation of the global solar radiation for any latitude in Egypt

The aim of this study is to obtain a nonlinear equation for computation of the monthly solar radiation for any latitude of any place in Egypt, when the recording solar instruments are not available. This equation allows to estimate the monthly values of the Global Solar Radiation for any latitude in Egypt with deviation from the published data (in the world net work), for any month, of about 17%.

Impact of Load Retention on Aircraft Engine Parts Under Real Flight Cycle Conditions in Service Life Monitoring

One of the major problems in the development of algorithms for monitoring the life of aircraft gas turbine engines is that the character of loading in real flight cycles is crucially different from the character of the static and dynamic loading during the testing of samples. This paper proposes a method for taking into account the effect of retentions at maximum stresses and cycle temperatures on the low-cycle fatigue (LCF) of the heat-resistant alloys used in engine parts. Regularities in repeated-static loading (RSL) are used in combination with the method of linear accumulation of damage due to the LCF and RSL, with retentions of a variable length. A non-linear equation is derived for the summation of these damages, the solution of which determines the durability (life) of the part while taking into account the retention duration. The theoretical results were verified by using the experimental characteristics of the GS-6K and EI-437B nickel-based alloys, previously reported by other researchers.

Emergent universe in $$D \ge 4$$ dimensions with dynamical wormholes

We present a flat emergent universe (EU) in Einstein gravity with non-linear equation of state (nEoS) in the usual four and in higher dimensions. The EU is assumed to evolve from an initial Einstein’s static universe (ESU) in the infinite past. For a homogeneous Ricci scalar we determine the shape function and obtain a new class of dynamical wormholes that permits EU. The nEoS $$p= A\rho -B \sqrt{\rho _o \rho }$$ p = A ρ - B ρ o ρ is equivalent to three different cosmic fluids which is identified with barotropic fluid for a given A. We obtain EU models in flat, closed and open universes and tested the null energy condition (NEC). At the throat of the wormhole which is recognized as the seed of ESU, we tested the NEC for a given size of the neck. As the EU evolves from an asymptotic past and approaches $$t=0$$ t = 0 , it is found that NEC does not respect. This triggers the onset of interactions at $$t=t_i$$ t = t i , and a realistic flat EU scenario can be obtained in four and in higher dimensions. The origin of the ESU at the throat of the wormhole is also explored via a gravitational instanton mechanism. We compare the relative merits of dynamical wormholes for implementing EU.

Analytical and numerical methods for calculation the deep of penetration the welding seam formed by the electron beam generated by glow discarge electron guns

The article is devoted to the problem of defining the focal diameter of electron beam, formed by the glow discharge electron guns, as well as the necessary pressure in the gun chamber for realising the welding process. Taking into account, that glow discharge electron guns are widely used in industry for welding of different metals, and that for providing the high quality of welding joints estimation of energetic parameters in beam focus is very important, proposed methods are very important for effective elaboration and designing of the novel glow discharge electron guns constructions for specific technological operations. With known focal beam deameter and thermodinamic parameters of welding details material the deep of penetration of welding seam, as well as the necessary pressure in discharge chamber have been estimatied. Two proposed methods are generally based on the analytical solving of explite equation and on numeracal solving of sophisticated non-linear equation. Obtained simulation results with and without taking into account the spsace charge of own beam electrons are also given

Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour

In this paper, we deal with some applications of the network simulation method (NMS) to the non-linear differential equations derived of a parametric family associated to stated problems by Newton in and others like the parabolic mirror and van der Pol non-linear equation. We underly the efficientcy of the (NMS) method, compare it with Matlab procedures and present figures of solutions of the equations obtained by it on the mentioned problems. Additionally, we introduce also the electric-electronic circuits we have designed to be able of obtaining the solutions of the referred equations.

The Stochastic Modified Lundqvist-Korf Diffusion Process: Statistical and Computational Aspects and Application to Modeling of the CO2 Emission in Morocco

The main goal of this paper is to study the possibility of using a stochastic non-homogeneous (without exogenous factors) diffusion process to model the evolution of CO2 emissions in Morocco and concretely using a new process, in which the trend function is proportional to the modified Lundqvist-Korf growth curve. First, the main characteristics of the process are studied, then we establish a computational statistical methodology based on the maximum likelihood estimation method and the trend functions. When we are estimating the parameters of the process, a non-linear equation is obtained and the simulated annealing method is proposed to solve it after bounding the parametric space by a stagewise procedure. Also, to validate this methodology, we include the results obtained from several examples of simulation. Finally, the process and the methodology established are applied to real data corresponding to the evolution of CO2 emissions in Morocco.

Assessment of Dynamic Properties of Variable Area Flowmeters

In previous works, a non-linear equation describing variable area (VA) flowmeters in transient was presented. The use of a full nonlinear equation, despite giving accurate results, can be difficult and time-consuming and it requires having specific software and knowledge at one’s disposal. The goal of this paper was to simplify the existing model so that it could be used in applications where ease of use and ease of implementation are more important than accuracy. The existing model was linearized and simple formulae describing natural frequency and damping coefficients were derived. With these parameters, it is possible to assess the dynamic properties of a variable area flowmeter. The step response form can be identified and natural frequency and settling time can be estimated. The linearized model and the experiment were in reasonable agreement. The step response type was captured correctly for each of the six VA meter types. The error in the undamped natural frequency was not larger than 15%, which means that the VA meter sensor’s dynamic properties can be predicted at the design stage with sufficient precision.

Using Iterative Reweighting Algorithm and Genetic Algorithm to Calculate The Estimation of The Parameters Of The Maximum Likelihood of The Skew Normal Distribution

Excessive skewness which occurs sometimes in the data is represented as an obstacle against normal distribution. So, recent studies have witnessed activity in studying the skew-normal distribution (SND) that matches the skewness data which is regarded as a special case of the normal distribution with additional skewness parameter (α), which gives more flexibility to the normal distribution. When estimating the parameters of (SND), we face the problem of the non-linear equation and by using the method of Maximum Likelihood estimation (ML) their solutions will be inaccurate and unreliable. To solve this problem, two methods can be used that are: the genetic algorithm (GA) and the iterative reweighting algorithm (IR) based on the Maximum Likelihood method. Monte Carlo simulation was used with different skewness levels and sample sizes, and the superiority of the results was compared. It was concluded that (SND) model estimation using (GA) is the best when the samples sizes are small and medium, while large samples indicate that the (IR) algorithm is the best. The study was also done using real data to find the parameter estimation and a comparison between the superiority of the results based on (AIC, BIC, Mse and Def) criteria.