摘要：In this paper, we apply Picard operator theory to investigate a class of fractional differential equations with iterations of linear modification of the argument. For that, two useful work spaces C L ( J , J ) and C L , θ ( J , J ) with three powerful norms ∥ ⋅ ∥ B , ∥ ⋅ ∥ β and ∥ ⋅ ∥ C are used, respectively. Some existence and uniqueness results are presented. Here, we introduce a new norm ∥ ⋅ ∥ β and give another direct way to deal with the iterative term in the nonlinear term, which can be regarded as the main novelty in this paper. MSC:26A33, 34A12, 47H10.
关键词：fractional order differential equations ; iterations ; existence ; Picard operator
