1. Anh V.V., Leonenko N.N. Spectral analysis of fractional kinetic eq\-uations with random data. J. Statist. Phys. 2001, 104 (5-6), 1349-1387. doi: 10.1023/A:1010474332598
  2. Djrbashian M.M., Nersessyan A.B. Fractional derivatives and Cauchy problem for differentials of fractional order. Izv. Akad. Nauk Arm. SSR. Ser. Mat. 1968, 3, 3-29.
  3. Duan J.-Sh. Time- and space-fractional partial differential equations. J. Math. Phys. 2005, 46 (1), 013504. doi: 10.1063/1.1819524
  4. Eidelman S.D., Ivasyshen S.D., Kochubei A.N. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. In: Operator Theory: Advances and Applications, 152. Birkhäuser Verlag, Basel-Boston-Berlin, 2004. doi: 10.1007/978-3-0348-7844-9
  5. Voroshylov A.A., Kilbas A.A. Conditions of the existence of classical solution of the Cauchy problem for diffusion-wave equation with Caputo partial derivative. Dokl. Akad. Nauk. 2007, 414 (4), 1-4. (in Russian)
  6. Lopushanska H.P., Lopushansky A.O. Space-time fractional Cauchy problem in spaces of generalized function. Ukrainian Math. J. 2013, 64 (8), 1215-1230. doi: 10.1007/s11253-013-0711-z (translaition of Ukrain. Mat. Zh. 2012, 64 (8), 1067-1080. (in Ukrainian))
  7. Lopushansky A.O. The Cauchy problem for an equation with fractional derivatives in Bessel potential spaces. Siberian Math. J. 2014, 55 (6), 1089-1097. doi: 10.1134/S0037446614060111 (translaition of Sibirsk. Mat. Zh. 2014, 55 (6), 1334-1344. (in Russian))
  8. Cheng J., Nakagawa J., Yamamoto M., Yamazaki T. Uniqueness in an inverse problem for a one-dimentional fractional diffusion equation. Inverse Problems 2009, 25 (11), 1-16. doi: 10.1088/0266-5611/25/11/115002
  9. Hatano Y., Nakagawa J., Wang Sh., Yamamoto M. Determination of order in fractional diffusion equation. Journal of Math-for-Industry 2013, 5A, 51-57.
  10. Nakagawa J., Sakamoto K., Yamamoto M. Overview to mathematical analysis for fractional diffusion equation - new mathematical aspects motivated by industrial collaboration. Journal of Math-for-Industry 2010, 2A, 99-108.
  11. Rundell W., Xu X., Zuo L. The determination of an unknown boundary condition in fractional diffusion equation. Appl. Anal. 2013, 92 (7), 1511-1526. doi: 10.1080/00036811.2012.686605
  12. Zhang Y. and Xu X. Inverse source problem for a fractional diffusion equation. Inverse Problems. 2011, 27 (3), 1-12. doi: 10.1088/0266-5611/27/3/035010
  13. Srivastava H.M., Gupta K.C., Goyal S.P. The H-functions of one and two variables with applications. South Asian Publishers, New Dehli, 1982.
  14. Kilbas A.A., Sajgo M. H-Transforms: Theory and Applications. Chapman and Hall/CRC, Boca-Raton, 2004.
  15. Lopushansky A.O. Regularity of the solutions of the boundary value problems for diffusion-wave equation with generalized functions in right-hand sides. Carpathian Math. Publ. 2013, 5 (2), 279-289. doi: 10.15330/cmp.5.2.279-289 (in Ukrainian)


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