Impulsive Noise Driven One-Dimensional Higher-Order Fractional Partial Differential Equations |
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Authors: | Bin Xie |
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Institution: | 1. International Young Researchers Empowerment Center , Shinshu University , Nagano, Japan;2. Department of Mathematical Sciences, Faculty of Science , Shinshu University , Nagano, Japan bxie@shinshu-u.ac.jp |
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Abstract: | We are going to study a kind of stochastic fractional partial differential equation driven by an impulsive noise, which is singular not only in time but also in space. We first study the existence and uniqueness of the solution and then investigate the regularity of the solution in its spatial variable which depends on the order of the fractional operator, and deeply relies on the precise analysis of the kernel generated by our operator. In addition, we also discuss the stochastic flow property of the solutions. |
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Keywords: | Existence and uniqueness Fractional differential equation Impulsive noise Regularity Stochastic flow |
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