Zhanbing Bai, Shuo Zhang, Sujing Sun, Chun Yin
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
where
,
,
is the standard Riemann-Liouville fractional
derivative,
.
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.
Submitted October 14, 2015. Published January 6, 2016.
Math Subject Classifications: 34B15, 34A08.
Key Words: Fractional initial value problem; lower and upper solution method;
existence of solutions.
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Zhanbing Bai College of Mathematics and System Science Shandong University of Science and Technology Qingdao 266590, China email: zhanbingbai@163.com | |
Shuo Zhang College of Mathematics and System Science Shandong University of Science and Technology Qingdao 266590, China email: 18353250431@163.com | |
Sujing Sun College of Information Science and Engineering Shandong University of Science and Technology Qingdao 266590, China email: kdssj@163.com | |
Chun Yin School of Automation Engineering University of Electronic Science and Technology of China Chengdu 611731, China email: yinchun.86416@163.com |
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