A class of nonlinear differential equations with fractional integrable impulses

作者：Wang, JinRong^*; Zhang, Yuruo

来源：Communications in Nonlinear Science & Numerical Simulation, 2014, 19(9): 3001-3010.

DOI：10.1016/j.cnsns.2014.01.016

• Impulsive differential equations
• Solutions
• Bielecki-Ulam's type stability

In this paper, we introduce a new class of impulsive differential equations, which is more suitable to characterize memory processes of the drugs in the bloodstream and the consequent absorption for the body. This fact offers many difficulties in applying the usual methods to analysis and novel techniques in Bielecki's normed Banach spaces and thus makes the study of existence and uniqueness theorems interesting. Meanwhile, new concepts of Bielecki-Ulam's type stability are introduced and generalized Ulam-Hyers-Rassias stability results on a compact interval are established. This is another novelty of this paper. Finally, an interesting example is given to illustrate our theory results.

• 出版日期2014-9
• 单位贵州大学; 贵州师范学院