Monotone iterative method for fractional differential equations
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Date
2016-01-06
Authors
Bai, Zhanbing
Zhang, Shuo
Sun, Sujing
Yin, Chun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, by using the lower and upper solution method, we prove the existence of iterative solutions for a class of fractional initial value problem with non-monotone term
Dα0+ u(t) = ƒ(t, u(t)), t ∈ (0, h),
t1-α u(t)|t=0 = u0 ≠ 0,
where 0 < h < +∞, ƒ ∈ C([0, h] x ℝ, ℝ), Dα0+ u(t) is the standard Riemann-Liouville fractional derivative, 0 < α < 1. A new condition on the nonlinear term is given to guarantee the equivalence between the solution of the IVP and the fixed-point of the corresponding operator. Moreover, we show the existence of maximal and minimal solutions.
Description
Keywords
Fractional initial value problem, Lower and upper solution method, Existence of solutions
Citation
Bai, Z., Zhang, S., Sun, S., & Yin, C. (2016). Monotone iterative method for fractional differential equations. Electronic Journal of Differential Equations, 2016(06), pp. 1-8.
Rights
Attribution 4.0 International