On fractional resolvent operator functions

By Chuang Chen, Miao Li. 2010

88 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/cf64d8f282e7790d96061d7b25295289cc229b72

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In Applied Mathematics

1. Yongxiang Li
2. Pengyu Chen
3. Xuping Zhang
4. Junxiong Jia
5. Jigen Peng
6. Kexue Li

In Control and Systems Engineering

1. Pengyu Chen
2. Yongxiang Li
3. Xuping Zhang
4. Jigen Peng
5. Kexue Li

In Modeling and Simulation

1. Yongxiang Li
2. Pengyu Chen
3. Xuping Zhang
4. Jigen Peng
5. Kexue Li

Citations in the corpus

• On fractional powers of generators of fractional resolvent families (2010, unknown): “generator A, then for t > 0, (2.9) Sα(t) = 1 2πi Z Γθ0 eλtλα−1(λα −A)−1dλ, where Γθ0 is any piecewise smooth curve in Σπ/2+θ going from ∞e −i(π/2+θ0) to ∞ei(π/2+θ0) for some 0 < θ 0 < θ (cf. [3, 8]). The following subordination principle is important in the theory of fractional resolvent fa”
• Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators (2020, background): “It is proved in [10] that a family Tα(t) (t ≥ 0) is an α-order fractional resolvent operator if and only if it is a solution operator for some fractional abstract Cauchy problem.”
• Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives ✩ (2012, background): “Chen and Li [5] presented a purely algebraic notion, α-resolvent operator function.”
• Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator (2018, unknown): “Application We recall that for a Banach’s space X , a one parameter family {Uα (t)}t≥0, α > 0 in B (X ) , the space of all bounded linear operators, is called an α−resolvent operator function if the following conditions are satisfied [39]: (1) Uα (t) is strongly continuous on R + and Uα (0) = I; (2)”
• A novel characteristic of solution operator for the fractional abstract Cauchy problem (2012, background): “Recently, Chen and Li [3] found a novel characteristic of solution operator, and thereby developed a purely algebraic notion, named α-resolvent operator function.”