Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations. (8th July 2012)

• Record Type: Journal Article
• Authors: Li, Qiuping; Sun, Shurong; Zhao, Ping; Han, Zhenlai
• Other Names: Baleanu Dumitru Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-07-08
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/615230
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We discuss the initial value problem for the nonlinear fractional differential equation L ( D ) u = f ( t, u ), t ∈ ( 0, 1 ], u ( 0 ) = 0, where L ( D ) = D s n - a n - 1 D s n - 1 - ⋯ - a 1 D s 1, 0 < s 1 < s 2 < ⋯ < s n < 1, and a j < 0, j = 1, 2, …, n - 1, D s j is the standard Riemann-Liouville fractional derivative and f : [ 0, 1 ] × ℝ → ℝ is a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established.