An approximate method for numerical solution of fractional differential equations

2006 ◽  
Vol 86 (10) ◽  
pp. 2602-2610 ◽  
Author(s):  
Pankaj Kumar ◽  
Om Prakash Agrawal
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Approximate Method ◽  
Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Qingxue Huang ◽  
Fuqiang Zhao ◽  
Jiaquan Xie ◽  
Lifeng Ma ◽  
Jianmei Wang ◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
Numerical Approach ◽  
Principal Characteristic ◽  
Legendre Functions ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Fractional Differential

In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent.

Numerical Solution for a System of Fractional Differential Equations with Applications in Fluid Dynamics and Chemical Engineering

2017 ◽  
Vol 15 (5) ◽  
Author(s):  
Bijil Prakash ◽  
Amit Setia ◽  
Shourya Bose
Keyword(s):  
Fluid Dynamics ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Crucial Role ◽  
Chemical Engineering ◽  
Haar Wavelets ◽  
Fractional Differential

Abstract In this paper, a Haar wavelets based numerical method to solve a system of linear or nonlinear fractional differential equations has been proposed. Numerous nontrivial test examples along with practical problems from fluid dynamics and chemical engineering have been considered to illustrate applicability of the proposed method. We have derived a theoretical error bound which plays a crucial role whenever the exact solution of the system is not known and also it guarantees the convergence of approximate solution to exact solution.

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