scholarly journals Application of Said Ball Curve for Solving Fractional Differential-Algebraic Equations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1926
Author(s):  
Fateme Ghomanjani ◽  
Samad Noeiaghdam
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Convergence Theorem ◽  
Differential Algebraic Equations ◽  
Bézier Curve ◽  
Algebraic Equations ◽  
Fractional Order Differential Equations ◽  
Curve Method ◽  
Fractional Differential

The aim of this paper is to apply the Said Ball curve (SBC) to find the approximate solution of fractional differential-algebraic equations (FDAEs). This method can be applied to solve various types of fractional order differential equations. Convergence theorem of the method is proved. Some examples are presented to show the efficiency and accuracy of the method. Based on the obtained results, the SBC is more accurate than the Bezier curve method.

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 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.

scholarly journals An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1755
Author(s):  
M. S. Al-Sharif ◽  
A. I. Ahmed ◽  
M. S. Salim
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Fractional Differential

Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

scholarly journals Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 96 ◽  
Author(s):  
İbrahim Avcı ◽  
Nazim I. Mahmudov
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Main Idea ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Fractional Order Differential Equations ◽  
Fractional Differential ◽  
The Given

In this article, we propose a numerical method based on the fractional Taylor vector for solving multi-term fractional differential equations. The main idea of this method is to reduce the given problems to a set of algebraic equations by utilizing the fractional Taylor operational matrix of fractional integration. This system of equations can be solved efficiently. Some numerical examples are given to demonstrate the accuracy and applicability. The results show that the presented method is efficient and applicable.

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.

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.

scholarly journals Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 914
Author(s):  
Oana Brandibur ◽  
Roberto Garrappa ◽  
Eva Kaslik
Keyword(s):  
Differential Equations ◽  
Detailed Analysis ◽  
Linear Systems ◽  
Fractional Order ◽  
Numerical Experiments ◽  
Limit Case ◽  
Fractional Order Differential Equations ◽  
Fractional Differential ◽  
The Stability

Systems of fractional-order differential equations present stability properties which differ in a substantial way from those of systems of integer order. In this paper, a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative is proposed. Starting from the well-known Matignon’s results on stability of single-order systems, for which a different proof is provided together with a clarification of a limit case, the investigation is moved towards multi-order systems as well. Due to the key role of the Mittag–Leffler function played in representing the solution of linear systems of FDEs, a detailed analysis of the asymptotic behavior of this function and of its derivatives is also proposed. Some numerical experiments are presented to illustrate the main results.

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