Approximate solution of fractional integro-differential equations by Taylor expansion method

作者：Huang, Li^*; Li, Xian Fang; Zhao, Yulin; Duan, Xiang Yang

来源：Computers & Mathematics with Applications, 2011, 62(3): 1127-1134.

DOI：10.1016/j.camwa.2011.03.037

• Fractional integro-differential equation
• Taylor expansion
• Approximate solution
• Riemann-Liouville
• Fredholm equations
• Volterra equations

In this paper, Taylor expansion approach is presented for solving (approximately) a class of linear fractional integro-differential equations including those of Fredholm and of Volterra types. By means of the mth-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.

• 出版日期2011-8
• 单位湖南工业大学; 中南大学