Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 17, Issue 12, Pages 5143-5150Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2012.03.036
Keywords
Semilinear fractional differential equation; Mittag-Leffler function; Integral operator; Integral inequality
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Funding
- Natural Science Foundation of China [11071192]
- International Science and Technology (S&T) Cooperation Program of China [2010DFA14700]
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Semilinear fractional differential equations (SFDEs) often arise in some dynamical systems. In most of the existing literature, the fixed point theorems are used to prove the existence and uniqueness of the solutions of SFDEs. In this paper, we give a new way to prove the existence and uniqueness of the solutions by introducing a new integral operator associated with the Mittag-Leffler function. (C) 2012 Elsevier B.V. All rights reserved.
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