An undetermined timedependent coefficient in a fractional diffusion equation
Pages: 875  900,
Issue 5,
October
2017
doi:10.3934/ipi.2017041 Abstract
References
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Zhidong Zhang  Department of Mathematics, Texas A&M University, College Station, TX 778433368, 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, 223276. 

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), 197221. 

4 
B. Jin and W. Rundell, An inverse problem for a onedimensional timefractional 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 NorthHolland Mathematics Studies, Elsevier Science B.V., Amsterdam, 2006. 

6 
Y. Lin and C. Xu, Finite difference/spectral approximations for the timefractional diffusion equation, J. Comput. Phys., 225 (2007), 15331552. 

7 
Y. Luchko, Maximum principle for the generalized timefractional diffusion equation, J. Math. Anal. Appl., 351 (2009), 218223. 

8 
K. S. Miller and S. G. Samko, Completely monotonic functions, Integral Transform. Spec. Funct., 12 (2001), 389402. 

9 
H. Pollard, The completely monotonic character of the MittagLeffler function $E_a(x)$, Bull. Amer. Math. Soc., 54 (1948), 11151116. 

10 
K. Sakamoto and M. Yamamoto, Initial value/boundary value problems for fractional diffusionwave equations and applications to some inverse problems, J. Math. Anal. Appl., 382 (2011), 426447. 

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'skiĭ, Translated from the 1987 Russian original, Revised by the authors. 

12 
W. R. Schneider, Completely monotone generalized MittagLeffler functions, Exposition. Math., 14 (1996), 316. 

13 
Z. Zhang, An undetermined coefficient problem for a fractional diffusion equation, Inverse Problems, 32 (2016), 015011, 21pp. 

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