Existence and uniqueness of a solution for a fractional differential equation by Rothe's method
A. Raheem, D. Bahuguna
Department Of Mathematics And Statistics, Indian Institute Of Technology Kanpur, Kanpur - 208016, India.
Received on August 1, 2012; Revised version: November 16, 2012
Accepted on November 16, 2012
Communicated by Gaston M. N'Guérékata
| Abstract. In this paper, we establish the existence and uniqueness of a strong solution for a semilinear fractional differential equation by using Rothe’s method. Thereafter, we show the continuous dependence of the solution on the initial data and the stability of the solution. | |
| Keywords: | Rothe’s method; Fractional differential equation; Strong solution; a priori estimate. |
| 2010 Mathematics Subject Classification: 34A08, 35D35, 34K06, 65M20, 34K20, 34A12. | |