In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2012 ( 2012), p. 1-14
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.
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2012
detail.hit.zdb_id:
2064801-7
SSG:
17,1
Permalink
