On a new class of impulsive fractional differential equations. (English) Zbl 1334.34022
Summary: We consider fractional ordinary differential equations with not instantaneous impulses. Firstly, we construct a uniform framework to derive a formula of solutions for impulsive fractional Cauchy problem involving generalization of classical Caputo derivative with the lower bound at zero. In other words, we mean a different solution keeping in each impulses the lower bound at zero, which can better characterize the memory property of fractional derivative. Secondly, we introduce a new concept of generalized Ulam-Hyers-Rassias stability. Then, we choose a fixed point theorem to derive a generalized Ulam-Hyers-Rassias stability result for such new class of impulsive fractional differential equations. Finally, an example is given to illustrate our main results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34A37 | Ordinary differential equations with impulses |
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