A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation

作者：Amairi M^*; Aoun M; Najar S; Abdelkrim M N

来源：Applied Mathematics and Computation, 2010, 217(5): 2162-2168.

DOI：10.1016/j.amc.2010.07.015

• Fractional order differential equations
• Caputo fractional derivative
• Initial value problems
• Existence and uniqueness
• Interval analysis
• Validated computing

This paper presents a new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations. An algorithm selecting a stepsize and computing a priori constant enclosure of the solution is proposed. Several illustrative examples, with linear and nonlinear fractional differential equations, are given to demonstrate the effectiveness of the method.

• 出版日期2010-11-1