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## Full-Text Articles in Education

Approximate Solution Of Fractional Integro-Differential Equations By Taylor Expansion Method, Li Huang

#### Approximate Solution Of Fractional Integro-Differential Equations By Taylor Expansion Method, Li Huang

*Li Huang*

In this paper, Taylor expansion approach is presented for solving (approximately) a class of inear fractional integro-differential equations including those of Fredholm and of Volterra types. By means of themth-order Taylor expansion of the unknown function at an arbitrary point, the linear fractional integro-differential equation can be converted approximately to a system of equations for the unknown function itself and its m derivatives under initial conditions. This method gives a simple and closed form solution for a linear fractional integro-differential equation. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.

Approximate Solution Of Abel Integral Equation, Li Huang

#### Approximate Solution Of Abel Integral Equation, Li Huang

*Li Huang*

This paper presents a new, stable, approximate inversion of Abel integral equation. By using the Taylor expansion of the unknown function, Abel equation is approximately transformed to a system of linear equations for the unknown function together with its derivatives. A desired solution can be determined by solving the resulting system according to Cramer’s rule. This method gives a simple and closed form of approximate Abel inversion, which can be performed by symbolic computation. The nth-order approximation is exact for a polynomial of degree up to n. Abel integral equation is approximately expressed in terms of integrals of input data; …

A New Abel Inversion By Means Of The Integrals Of An Input Function With Noise, Li Huang

#### A New Abel Inversion By Means Of The Integrals Of An Input Function With Noise, Li Huang

*Li Huang*

Abel’s integral equations arise inmany areas of natural science and engineering, particularly in plasma diagnostics. This paper proposes a new and effective approximation of the inversion of Abel transform. This algorithm can be simply implemented by symbolic computation, and moreover an nth-order approximation reduces to the exact solution when it is a polynomial in r2 of degree less than or equal to n. Approximate Abel inversion is expressed in terms of integrals of input measurement data; so the suggested approach is stable for experimental data with random noise. An error analysis of the approximation of Abel inversion is given. Finally, …