scholarly journals RELIABILITY ANALYSIS OF THE UNCERTAIN FRACTIONAL-ORDER DYNAMIC SYSTEM WITH STATE CONSTRAINT

2021 ◽  
Author(s):  
Ting Jin ◽  
Hongxuan Xia ◽  
Shangce Gao
Keyword(s):  
Dynamic System ◽  
Reliability Analysis ◽  
Fractional Order ◽  
Uncertain System ◽  
State Constraint ◽  
Barrier Option ◽  
Initial State ◽  
Expected Time ◽  
Liu Process ◽  
Predictor Corrector

Uncertain fractional-order differential equations driven by Liu process are of significance to depict the heredity and memory features of uncertain dynamical systems. This paper primarily investigates the reliability analysis of the uncertain fractional-order dynamic system with a state constraint. On the basis of the first-hitting time (FHT), a novel uncertain fractional-order dynamic system considering a state constraint is proposed. Secondly, in view of the relation between the initial state and the required standard, such uncertain fractional-order dynamic systems are subdivided into four types. The concept of reliability of proposed uncertain system with a state constraint is presented innovatively. Corresponding reliability indexes are ulteriorly formulated via FHT theorems. Lastly, the uncertain fractional-order dynamic system with a state constraint is applied to different physical and financial dynamical models. The analytic expression of the reliability index is derived to demonstrate the reasonableness of our model. Meanwhile, expected time response and American barrier option prices are calculated by using the predictor-corrector scheme. A sensitivity analysis is also illustrated with respect to various conditions.

Lassa hemorrhagic fever model using new generalized Caputo-type fractional derivative operator

2021 ◽  
pp. 2150055
Author(s):  
Pushpendra Kumar ◽  
Vedat Suat Erturk ◽  
Abdullahi Yusuf ◽  
Tukur Abdulkadir Sulaiman
Keyword(s):  
Pregnant Women ◽  
Fractional Order ◽  
Research Work ◽  
Hemorrhagic Fever ◽  
Hemorrhagic Disease ◽  
Lassa Virus ◽  
Research Fields ◽  
Negative Impacts ◽  
Predictor Corrector ◽  
The Given

In some of the previous decades, we have observed that mathematical modeling has become one of the most interesting research fields and has attracted many researchers. In this regard, thousands of researchers have proposed different varieties of mathematical models to study the dynamics of a number of real-world problems. This research work is framed to analyzing the structure of the well-known Lassa hemorrhagic epidemic; a dangerous epidemic for pregnant women, via new generalized Caputo type noninteger order derivative with the help of a modified Predictor–Corrector scheme. Lassa hemorrhagic disease is an epidemical and biocidal fever, whose negative impacts were initially recognized in the countries of Africa. This virus has killed many pregnant women as compared to the Ebola epidemic. It was noticed that Lassa virus was isolated in Vero cell cultures from a blood pattern, and after 12 days it was ejective, after the climb of the sickness. In this research study, necessary theorems and lemmas are reminded to prove the existence of a unique solution and stability of given fractional approximation scheme. All necessary results are reminded to confirm the effectiveness of the proposed approximation algorithm by graphical observations for various fractional-order values. In our practical calculations, we plotted the graphs for two different values of natural death rate along with various values of given fractional-order operator. Our major target is to show the importance of the proposed modified version of the Predictor–Corrector algorithm in epidemic studies by exploring the given Lassa hemorrhagic fever dynamics.

scholarly journals Reliability Analysis of a Filtering Reducer under the Discrete Space Environmental Shocks

2014 ◽  
Vol 6 ◽  
pp. 921720 ◽  
Author(s):  
Jing Lu ◽  
Zhonglai Wang ◽  
Wei Chen ◽  
Xuefei Zhang ◽  
Hao Liu
Keyword(s):  
Differential Equations ◽  
Dynamic System ◽  
Mechanism Design ◽  
Reliability Analysis ◽  
Dynamic Model ◽  
Space Environment ◽  
Newmark Method ◽  
Lumped Mass ◽  
Dynamic Reliability ◽  
Environmental Shocks

Dynamic reliability analysis of a filtering reducer is performed by accounting for discrete shocks from the space environment. Gears are considered as the lumped mass and meanwhile the meshing between different gears is equivalent to a dynamic system consisting of springs and dampers during construction of the dynamic model. The Newmark method is employed to resolve differential equations, and then the additional acceleration could be obtained, caused by shocks to the filtering reducer. Dynamic reliability analysis is conducted with the help of the Simulink tool for the outputs. The results are hopefully useful for spacecraft mechanism design.

Dynamics analysis of fractional-order Hopfield neural networks

2020 ◽  
pp. 2050083
Author(s):  
Iqbal M. Batiha ◽  
Ramzi B. Albadarneh ◽  
Shaher Momani ◽  
Iqbal H. Jebril
Keyword(s):  
Neural Network ◽  
Lyapunov Exponents ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Phase Portraits ◽  
Dynamics Analysis ◽  
Fractional Order Systems ◽  
Runge Kutta Method ◽  
Intermittent Chaos ◽  
Predictor Corrector

This paper proposes fractional-order systems for Hopfield Neural Network (HNN). The so-called Predictor–Corrector Adams–Bashforth–Moulton Method (PCABMM) has been implemented for solving such systems. Graphical comparisons between the PCABMM and the Runge–Kutta Method (RKM) solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems. To determine all Lyapunov exponents for them, the Benettin–Wolf algorithm has been involved in the PCABMM. Based on such algorithm, the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described, the intermittent chaos for these systems has been explored. A new result related to the Mittag–Leffler stability of some nonlinear Fractional-order Hopfield Neural Network (FoHNN) systems has been shown. Besides, the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents’ diagrams.

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