Fractional evolution equations in Banach spaces

By Emilia G. Bazhlekova. 2001

719 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9364cd11d1479bb40d8f00c7e98d36bdde289595

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yuri Luchko
2. Anatoly N. Kochubei
3. Masahiro Yamamoto
4. Yongxiang Li
5. Pengyu Chen
6. Mark M. Meerschaert
7. Carlos Lizama
8. Yong Zhou

In Modeling and Simulation

1. Mark M. Meerschaert
2. Yuri Luchko
3. Masahiro Yamamoto
4. Carlos Lizama
5. Charles Tadjeran
6. Anatoly N. Kochubei
7. Yongxiang Li
8. Hans-Peter Scheffler

In Numerical Analysis

1. Yuri Luchko
2. Masahiro Yamamoto
3. Mark M. Meerschaert
4. Carlos Lizama
5. Anatoly N. Kochubei
6. Charles Tadjeran
7. Yongxiang Li
8. Yong Zhou

Citations in the corpus

• Stochastic delay fractional evolution equations driven by fractional Brownian motion (2014, background): “1 in [24]), it follows that A generates an exponentially bounded solution operator T ̨.”
• Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2) (2019, background): “Bajlekova [12] exploited the concept of the fractional resolvent solution operator to investigate the associated fractional abstract Cauchy problem.”
• Controllability of Fractional Differential Equation of Order α∈(1,2] With Non‐Instantaneous Impulses (2018, background): “[14] A family (Cα(t))t≥0 ⊂ L(X ), α ∈ (1, 2] is called the solution operator (or a strongly continuous α-order fractional cosine family) for (2) and A is called the infinitesimal generator of Cα(t) if the following conditions hold:”
• Time-fractional diffusion equation in the fractional Sobolev spaces (2015, methodology): “It is worth mentioning that in [2], [28], and [29], the fractional differential equations with the Riemann-Liouville (and not the Caputo) fractional derivative and the related integro-differential equations were studied.”
• Hölder continuous solutions for fractional differential equations and maximal regularity (2013, background): “approaches to the existence and uniqueness of solutions to fractional differential equations can be found, for example, in [6, 9, 13, 17, 20, 32].”
• A second-order accurate numerical approximation for the fractional diffusion equation (2006, background): “It may also be possible to develop a similar theory for the fractional diffusion equation using the fact that the Mittag–Leffler functions are the eigenfunctions of the Caputo fractional derivative [1].”