Nonlocal Cauchy problem for fractional evolution equations
567 citations recorded by the source corpus.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/e41be252df3e9b45049a1313bf9d1faeec907e6a
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In Applied Mathematics
- V. Vijayakumar
- R. Udhayakumar
- Kottakkaran Sooppy Nisar
- Chokkalingam Ravichandran
- Jinrong Wang
- Yongxiang Li
- Yong Zhou
- Michal Feckan
In Modeling and Simulation
- V. Vijayakumar
- R. Udhayakumar
- Kottakkaran Sooppy Nisar
- Chokkalingam Ravichandran
- Jinrong Wang
- Yongxiang Li
- Michal Feckan
- Yong Zhou
Citations in the corpus
- Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions (2014, background): “Motivated by [22, 32, 40], we give the definition of mild solution to (1)–(2).”
- Controllability for fractional evolution inclusions without compactness (2015, background): “[30, 33] The operators T and S have the following properties: (i) for any fixed t ≥ 0, T (t) and S (t) are linear and bounded operators, i.”
- Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces (2013, methodology): “[6] Y. Zhou and F. Jiao, “Existence of mild solutions for fractional neutral evolution equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1063–1077, 2010.”
- Abstract Cauchy problem for fractional differential equations (2013, background): “[19], and Zhou and Jiao [22], the compactness of {S(t), t ≥ 0} is omitted and the conditions on f are a nonlinear case and more general.”
- Existence of mild solutions for fractional evolution equations with mixed monotone nonlocal conditions (2013, background): “In the applications, we only need to verify the nonlinear term f and the nonlocal function g satisfy some monotonicity condition, which are more weak and easy to be verified than the growth condition which assumed in [14,16,17,19].”
- On the new concept of solutions and existence results for impulsive fractional evolution equations (2011, methodology): “In this paper we continue to combine these two areas and our works [16, 17, 33, 36] to extend the study to the Cauchy problems for impulsive fractional evolution equations: (1.”