1. Anh V.V., Leonenko N.N. Spectral analysis of fractional kinetic equations with random datas. J. Stat. Phys. 2001, 104 (5/6), 1349-1387.
  2. Caputo M. Linear model of dissipation whose Q is almost friequency independent, II. Geofis. J. R. Astr. Soc. 1967, 13, 529-539.
  3. Cheng J., Nakagawa J., Yamamoto M., Yamazaki T. Uniqueness in an inverse problem for a one-dimentional fractional diffusion equation. Inverse problems 2009, 25, 1-16.
  4. Djrbashian M.M. Integral transformations and representations of functions in complex domain. Nauka, Moscow, 1999. (in Russian)
  5. Duan Jun-Sheng. Time- and space-fractional partial differential equations. J. Math. Phys. 2005, 46 (1), 13504-13511.
  6. Eidelman S.D., Ivasyshen S.D., Kochubei A.N. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. Birkhäuser Verlag, Basel-Boston-Berlin, 2004.
  7. El-Borai M. M. On the solvability of an inverse fractional abstract Cauchy problem. Intern. J. Research Rev. Appl. Sci. 2010, 4, 411-415.
  8. Hatano Y., Nakagawa J., Wang Sh., Yamamoto M. Determination of order in fractional diffusion equation. J. Math. Ind. 2013, 5A, 51-57.
  9. Ivanchov M. Inverse problems for equations of parabolic type. In: Math. Studies, Monograph Ser., 10, VNTL Publ., Lviv, 2003.
  10. Kochubei A.N. Fractional-order diffusion. Differential Equations 1990, 26, 485-492.
  11. Kochubei A.N., Eidelman S.D. Equations of one-dimentional fractional-order diffusion. Reports NAS of Ukraine 2002, 12, 11-16. (in Ukrainian)
  12. Lopushanska H.P., Lopushanskyj A.O. Space-time fractional Cauchy problem in spaces of generalized functions. Ukr. Math. J. 2013 64 (8), 1215-1230. doi:10.1007/s11253-013-0711-z (translation of Ukr. Mat. Zhurn. 2012, 64 (8), 1067-1080. (in Ukrainian))
  13. 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)
  14. Luchko Yu. Boundary value problem for the generalized time-fractional diffusion equation of distributed order. Fract. Calc. Appl. Anal. 2009, 12, 409-422.
  15. Meerschaert M.M., Nane Erkan, Vallaisamy P. Fractional Cauchy problems on bounded domains. Ann. Probab. 2009, 37, 979-1007.
  16. Nakagawa J., Sakamoto K., Yamamoto M. Overview to mathematical analysis for fractional diffusion equation — new mathematical aspects motivated by industrial collaboration. J. Math. Ind. 2010, 2A, 99-108.
  17. Rundell W., Xu X., Zuo L. The determination of an unknown boundary condition in fractional diffusion equation. Appl. Anal. 2012, 1, 1-16.
  18. Shilov G.E. Mathimatical Analysis. Second special course. Nauka, Moscow, 1965. (in Russian)
  19. Vladimirov V.S. Equations of Mathematical Physics. Marcel Dekker, New York, 1971. (translation of Nauka, Moscow, 1967. (in Russian))
  20. 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. Ak. Nauk 2007, 414 (4), 1-4. (in Russian)
  21. Zhang Y., Xu X. Inverse source problem for a fractional diffusion equation. Inverse problems 2011, 27, 1-12.


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