An Efficient Method for Solving Systems of Linear Ordinary and Fractional Differential Equations

作者：Didgar Mohsen^*; Ahmadi Nafiseh

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38(4): 1723-1740.

DOI：10.1007/s40840-014-0060-6

• System of ordinary differential equations
• System of fractional differential equations
• Riemann-Liouville fractional derivative
• Taylor expansion

This paper presents a reliable approach for solving linear systems of ordinary and fractional differential equations. First, the FDEs or ODEs of a system with initial conditions to be solved are transformed to Volterra integral equations. Then Taylor expansion for the unknown function and integration method are employed to reduce the resulting integral equations to a new system of linear equations for the unknown and its derivatives. The fractional derivatives are considered in the Riemann-Liouville sense. Some numerical illustrations are given to demonstrate the effectiveness of the proposed method in this paper.

• 出版日期2015-10