Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2
By Linxin Shu, Xiao-Bao Shu, J. Mao. Fractional Calculus and Applied Analysis, 2019
111 citations recorded by the source corpus.
Abstract In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2. As far as we know, there are few articles investigating on this issue. Firstly, the mild solutions to the equations are proved using Laplace transform of the Riemann-Liouville derivative. Moreover, the estimations of resolve operators involving the Riemann-Liouville fractional derivative of order 1 < α < 2 are given. Then, the existence results are obtained via the noncompact measurement strategy and the Mönch fixed point theorem. The approximate controllability of this nonlinear Riemann-Liouville fractional nonlocal stochastic systems of order 1 < α < 2 is concerned under the assumption that the associated linear system is approximately controllable. Finally, the approximate controllability results are obtained by using Lebesgue dominated convergence theorem.
Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/ea4ff38a77f6c7d29eaf246b665229c892d8db89
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In Applied Mathematics
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In Control and Systems Engineering
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- Chokkalingam Ravichandran
In Modeling and Simulation
- Kottakkaran Sooppy Nisar
- V. Vijayakumar
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- S. K. Panda
- W. Kavitha Williams
- Chokkalingam Ravichandran
- M. Mohan Raja
- K. Kavitha
Citations in the corpus
- Existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2 (2020, background): “A broad list of the distributions related with discussion on the existence and controllability can be discovered in [7, 19–26, 29–31, 33–36, 39, 41, 44, 45, 48, 52–59].”