A. Chauhan, G. R. Gautam, Jitendra Kumar, J. Dabas, Chauhan S P S
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引用次数: 0
摘要
本文介绍了Lp (p> 2)空间中的脉冲随机分数阶微分方程。我们提出了一个寻找ISFDEs解的一般框架。然后，利用Burkholder - Davis - Gundy不等式和Holder不等式，用不动点定理证明了ISFDE解的存在唯一性。我们还利用Gronwall不等式研究了解关于初值的Lipschitz连续性。最后，我们提供了一个应用来说明我们得到的结果。
Stochastic fractional differential equations with generalized Caputo's derivative and impulsive effects
In this paper, impulsive stochastic fractional differential equations (ISFDEs) in Lp (p> 2) space are introduced. We present a general framework for finding solution for ISFDEs. Then, by using the Burkholder - Davis - Gundy inequality and Holder's inequality, we prove the existence and uniqueness of solution to ISFDE by fixed point theorem. We also investigate Lipschitz continuity of solutions with respect to initial values by using Gronwall inequality. Finally, we provide an application to illustrate the results we obtained.
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