Existence of mild solutions for fractional neutral evolution equations

By Yong Zhou, Feng Jiao. Computers and Mathematics with Applications, 2010

724 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/102a5268deb4891cfcf53bd66c2e35462878f5cb

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators (2020, background): “Since fractional order semilinear evolution equations are abstract formulations for many problems arising in engineering and physics, fractional evolution equations have attracted a large amount of attention in recent years, see [9, 13, 14, 15, 17, 19, 22, 23, 27, 28, 40, 41, 43, 44, 45, 48, 51] and”
Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions (2017, background): “([35]) For any γ ∈ (0, 1), η ∈ (0, 1], and ∀ x ∈ D(A) there exists a positive constant Cη such that APγ(t)x = A 1−ηPγ(t)Aηx, 0 ≤ t ≤ b, and ‖APγ(t)‖ ≤ γCηΓ(2− η) tγηΓ(1 + γ(1− η)) , 0 < t ≤ b.”
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].”
Fractional differential equations: a novel study of local and global solutions in Banach spaces (2013, methodology): “This new formula is quite used as a tool in fractional framework to prove some useful properties (see [62, 66, 79]).”
A New Investigation on Fractional-Ordered Neutral Differential Systems with State-Dependent Delay (2019, background): “(see [34]) Sp(9) and Tp(9) acquire the subsequent properties.”