Speaker : Hong Wang* and Xiangcheng Zheng** 

* University of South Carolina

** Shandong University 

Time : 15:00 - 16:00 CET (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube : https://youtu.be/hFKqEB4QrR0?feature=shared

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Fractional calculus, Variable exponent, Mathematical analysis, Numerical method

Abstract: Fractional differential equations of variable exponent provide adequate descriptions for complex phenomena, while rigorous mathematical and numerical analysis are far from well developed. We discuss several methods to treat typical variable-exponent fractional problems such as the time-fractional mobile-immobile diffusion equation, subdiffusion equation and fractional diffusion-wave equation. The well-posedness and regularity of these models are proved, and numerical analysis is accordingly performed. Furthermore, optimal control of variable-exponent fractional problems is proposed and analyzed. 

Biography: Hong Wang is a professor at University of South Carolina. His research interest includes numerical analysis and scientific computing in porous medium flow and fractional problems. He has more than 200 publications on journals such as SIAM J. Sci. Comput., SIAM J. Numer. Anal., SIAM J. Control Optim. and Multiscale Model. Simul.. 

Bibliography

[1] H. Wang and X. Zheng, Wellposedness and regularity of the variable-order time-fractional diffusion equations. J. Math. Anal. Appl. 475 (2019) 1778--1802. 

[2] X. Zheng and H. Wang, An error estimate of a numerical approximation to a hidden-memory variable-order space-time fractional diffusion equation. SIAM J. Numer. Anal. 58 (2020) 2492--2514. 

[3] X. Zheng and H. Wang, A hidden-memory variable-order fractional optimal control model: analysis and approximation. SIAM J. Control Optim. 59 (2021) 1851--1880. 

[4] X. Zheng and H. Wang, Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions. IMA J. Numer. Anal. 41 (2021) 1522--1545. 

[5] X. Zheng and H. Wang, A time-fractional partial differential equation with a space-time dependent hidden-memory variable order: analysis and approximation. BIT Numer. Math. 61 (2021) 1453--1481. 

[6]  X. Zheng, Two methods addressing variable-exponent fractional initial and boundary value problems and Abel integral equations. arXiv:2404.09421v2. 

[7] X. Zheng, Y. Li, W. Qiu, Local modification of subdiffusion by initial Fickian diffusion: Multiscale modeling, analysis and computation. Multiscale Model. Simul. 22 (2024), 1534--1557. 

[8] X. Zheng, H. Wang, W. Qiu, Numerical analysis for high-order methods for variable-exponent fractional diffusion-wave equation. arXiv:2406.02941.