An inverse problem for a one-dimensional time-fractional diffusion problem

By Bangti Jin, William Rundell. 2012

179 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Modeling and Simulation

How researchers see this paper

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

In Control and Systems Engineering

1. Guofei Pang
2. G. Em Karniadakis
3. Lu Lu
4. Suleyman Ulusoy
5. Erkan Nane
6. Maizar Raissi
7. Paris Perdikaris

In Mathematical Physics

1. Ngartelbaye Guerngar
2. G. Em Karniadakis
3. Lu Lu
4. Suleyman Ulusoy
5. Guofei Pang
6. Erkan Nane

In Modeling and Simulation

1. G. Em Karniadakis
2. Lu Lu
3. Suleyman Ulusoy
4. Guofei Pang
5. Ngartelbaye Guerngar
6. Erkan Nane
7. Zhiping Mao
8. Xuhui Meng

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “For inverse problems, little is known about 3D space-time-fractional ADEs with a fractional Laplacian, despite some existing works on 1D and 2D problems [41, 42, 43, 44, 45, 46].”
• Inverse problem for a three-parameter space-time fractional diffusion equation (2018, background): “While most of these works have been dedicated to fractional derivatives only in the time variable [3, 10, 13, 14, 17, 18, 22, 23, 24], space-time fractional derivatives were considered in [20, 21], similarly as in this article.”
• A UNIQUENESS RESULT FOR AN INVERSE PROBLEM IN A SPACE-TIME FRACTIONAL DIFFUSION EQUATION (2013, background): “Important references documenting the recent interest on inverse problems with fractional derivatives are [4, 6, 9, 10, 13, 14, 16, 17, 18].”
• A tutorial on inverse problems for anomalous diffusion processes (2015, unknown): “In [50], the authors considered the identification of a potential term from the lateral flux data at one fixed time instance corresponding to a complete set of source terms, and established the unique determination for “small” potentials.”