Solving variable-order fractional differential algebraic equations via generalized fuzzy hyperbolic model with application in electric circuit modeling

2020 ◽  
Vol 24 (22) ◽  
pp. 16745-16758 ◽  
Author(s):  
Marzieh Mortezaee ◽  
Mehdi Ghovatmand ◽  
Alireza Nazemi
Keyword(s):  
Electric Circuit ◽  
Differential Algebraic Equations ◽  
Hyperbolic Model ◽  
Circuit Modeling ◽  
Variable Order ◽  
Algebraic Equations ◽  
Fractional Differential ◽  
Generalized Fuzzy Hyperbolic Model

scholarly journals New efficiency algorithm for solving fractional order differential-algebraic system

2016 ◽  
Vol 5 (3) ◽  
pp. 152
Author(s):  
Sameer Hasan ◽  
Eman Namah
Keyword(s):  
Exact Solution ◽  
Fractional Order ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Algebraic System ◽  
Analytic Solution ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Differential Algebraic System ◽  
Fractional Differential

This work provided the evolution of the algorithm for analytic solution of system of fractional differential-algebraic equations (FDAEs).The algorithm referred to good effective method for combination the Laplace Iteration method with general Lagrange multiplier (LLIM). Through this method we have reached excellent results in comparison with exact solution as we illustrated in our examples.

Simple Recipe for Accurate Solution of Fractional Order Equations

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Sambit Das ◽  
Anindya Chatterjee
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Initial Conditions ◽  
Special Functions ◽  
Differential Algebraic Equations ◽  
Accurate Solution ◽  
Algebraic Equations ◽  
Matlab Program ◽  
Fractional Differential

Fractional order integrodifferential equations cannot be directly solved like ordinary differential equations. Numerical methods for such equations have additional algorithmic complexities. We present a particularly simple recipe for solving such equations using a Galerkin scheme developed in prior work. In particular, matrices needed for that method have here been precisely evaluated in closed form using special functions, and a small Matlab program is provided for the same. For equations where the highest order of the derivative is fractional, differential algebraic equations arise; however, it is demonstrated that there is a simple regularization scheme that works for these systems, such that accurate solutions can be easily obtained using standard solvers for stiff differential equations. Finally, the role of nonzero initial conditions is discussed in the context of the present approximation method.

scholarly journals An efficient scheme for solving a system of time- fractional order differential-algebraic equations by using fractional Laplace iteration method

2016 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
Sameer Hasan ◽  
Eman Namah
Keyword(s):  
Fractional Order ◽  
Iteration Method ◽  
Efficient Algorithm ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Efficient Scheme ◽  
Fractional Differential

In this article, we propose an efficient algorithm for solving system of time- fractional differential-algebraic equations by using a fractional Laplace iteration method. The scheme is tested for some examples and the results demonstrate reliability and accuracy of this method.

scholarly journals A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1134
Author(s):  
Yongpeng Tai ◽  
Ning Chen ◽  
Lijin Wang ◽  
Zaiyong Feng ◽  
Jun Xu
Keyword(s):  
Fractional Calculus ◽  
Sliding Mode Control ◽  
Numerical Method ◽  
Present Method ◽  
Sliding Mode ◽  
Constitutive Relations ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Mode Control ◽  
Fractional Differential

Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. However, most of the methods cannot be directly applied in the equations of dynamic systems. This paper presents a numerical algorithm of fractional differential-algebraic equations based on the theory of sliding mode control and the fractional calculus definition of Grünwald–Letnikov. The algebraic equation is considered as the sliding mode surface. The validity of the present method is verified by comparing with an example with exact solutions. The accuracy and efficiency of the present method are studied. It is found that the present method has very high accuracy and low time consumption. The effect of violation corrections on the accuracy is investigated for different time steps.

Waveform relaxation method for fractional differential-algebraic equations

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Xiao-Li Ding ◽  
Yao-Lin Jiang
Keyword(s):  
Integrated Circuits ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Relaxation Method ◽  
Differential Algebraic Equations ◽  
Iteration Scheme ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Waveform Relaxation Method ◽  
Fractional Differential

AbstractThe waveform relaxation method has been successfully applied into solving fractional ordinary differential equations and fractional functional differential equations [11, 5]. In this paper, the waveform relaxation method is further used to solve fractional differential-algebraic equations, which often arise in integrated circuits with new memory materials. We give the iteration scheme of the waveform relaxation method and analyze the convergence of the method under linear and nonlinear conditions for the right-hand of the equations. Numerical examples illustrate the feasibility and efficiency of the method.

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