J. Nonl. Evol. Equ. Appl. 2013 (4), pp. 43-54, published on April 11, 2013:

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.

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