Fractional Differential Equations
Fractional differential equations generalize ODEs and PDEs to include derivative operators of non-integer order. The resulting operators are generally nonlocal and thus pose several challenges to conventional numerical approaches.Fractional PDEs appear in natural science applications featuring memory effects, e.g. photoacoustic imaging in medical physics.
- A frame approach for equations involving the fractional Laplacian Ioannis P. A. Papadopoulos, T. S. Gutleb, J. A. Carrillo, S. Olver. arXiv
- Explicit fractional Laplacians and Riesz potentials of classical functions T. S. Gutleb, Ioannis P. A. Papadopoulos. arXiv
- A static memory sparse spectral method for time-fractional PDEs T. S. Gutleb, J. A. Carrillo. Journal of Computational Physics (2023). arXiv DOI