`a`
Inverse Problems and Imaging (IPI)
 

An undetermined time-dependent coefficient in a fractional diffusion equation
Pages: 875 - 900, Issue 5, October 2017

doi:10.3934/ipi.2017041      Abstract        References        Full text (668.4K)           Related Articles

Zhidong Zhang - Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States (email)

1 L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, 2nd edition, American Mathematical Society, Providence, RI, 2010.       
2 R. Gorenflo and F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, in Fractals and fractional calculus in continuum mechanics (Udine, 1996), vol. 378 of CISM Courses and Lectures, Springer, Vienna, 1997, 223-276.       
3 B. Jin, R. Lazarov and Z. Zhou, An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data, IMA J. Numer. Anal., 36 (2016), 197-221.       
4 B. Jin and W. Rundell, An inverse problem for a one-dimensional time-fractional diffusion problem, Inverse Problems, 28 (2012), 075010, 19pp.       
5 A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, 2006.       
6 Y. Lin and C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys., 225 (2007), 1533-1552.       
7 Y. Luchko, Maximum principle for the generalized time-fractional diffusion equation, J. Math. Anal. Appl., 351 (2009), 218-223.       
8 K. S. Miller and S. G. Samko, Completely monotonic functions, Integral Transform. Spec. Funct., 12 (2001), 389-402.       
9 H. Pollard, The completely monotonic character of the Mittag-Leffler function $E_a(-x)$, Bull. Amer. Math. Soc., 54 (1948), 1115-1116.       
10 K. Sakamoto and M. Yamamoto, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, J. Math. Anal. Appl., 382 (2011), 426-447.       
11 S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, 1993, Theory and applications, Edited and with a foreword by S. M. Nikol'skiń≠, Translated from the 1987 Russian original, Revised by the authors.       
12 W. R. Schneider, Completely monotone generalized Mittag-Leffler functions, Exposition. Math., 14 (1996), 3-16.       
13 Z. Zhang, An undetermined coefficient problem for a fractional diffusion equation, Inverse Problems, 32 (2016), 015011, 21pp.       

Go to top