References

  1. Krzysztof B., Jakubowski T. Estimates of heat kernel of fractional Laplacian perturbed by gradient operators. Comm. Math. Phys. 2007, 271, 179–198. doi:10.1007/s00220-006-0178-y
  2. Boyko M.V., Osypchuk M.M. Perturbation of a rotationally invariant \(\alpha\)-stable stochastic process by a pseudo-gradient operator. Precarpathian Bull. Shevchenko Sci. Soc.: Number. 2021, 16 (60), 20–32. doi:10.31471/2304-7399-2021-16(60)-20-32 (in Ukrainian)
  3. Eidelman S.D., Ivasyshen S.D., Kochubei A.N. Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type. In: Ball A.J., Böttcher A., Dym H., Langer H., Tretter C. (Eds.) Operator Theory: Advances and Applications, 152. Birkhäuser, Basel, 2004. doi:10.1007/978-3-0348-7844-9
  4. Erdelyi A. Higher transcendental functions, vol. II, Bateman Manuscript Project, New York, 1953.
  5. Friedman A. Partial Differential Equations of Parabolic Type. Prentice-Hall Inc., Englewood Cliffs, NJ., 1964.
  6. Jakubowski T. Fundamental solution of the fractional diffusion equation with a singular drift. J. Math. Sci. (N.Y.) 2016, 218 (2), 137–153. doi:10.1007/s10958-016-3016-6
  7. Loebus J.U., Portenko M.I. On one class of perturbations of the generators of a stable process. Theory Probab. Math. Statist. 1995, 52, 102–111. (in Ukrainian)
  8. Osypchuk M.M. On some perturbations of a symmetric stable process and the corresponding Cauchy problems. Theory Stoch. Process. 2016, 21(37) (1), 64–72.
  9. Osypchuk M.M. On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations. Carpathian Math. Publ. 2015, 7 (1), 101–107. doi:10.15330/cmp.7.1.101-107
  10. Osypchuk M.M., Portenko M.I. On simple-layer potentials for one class of pseudodifferential equations. Ukrainian Math. J. 2016, 67 (11), 1704–1720. doi:10.1007/s11253-016-1184-7
  11. Osypchuk M.M., Portenko M.I. Symmetric \(\alpha\)-stable stochastic process and the third initial-boundary-value problem for the corresponding pseudodifferential equation. Ukrainian Math. J. 2018, 69 (10), 1631–1650. doi:10.1007/s11253-018-1459-2
  12. Podolynny S.I., Portenko N.I. On multidimentional stable processes with locally unbounded drift. Random Oper. Stoch. Equ. 1995, 3 (2), 113–124. doi:10.1515/rose.1995.3.2.113
  13. Portenko N.I. Generalized Diffusion Processes. Translations of Mathematical Monographs, 83. American Mathematical Society, Providence, Rhode Island, 1990.
  14. Portenko N.I. Some perturbations of drift-type for symmetric stable processes. Random Oper. Stoch. Equ. 1994, 2 (3), 211–224. doi:10.1515/rose.1994.2.3.211
  15. Portenko N.I. One class of transformations of a symmetric stable process. Theory Stoch. Process. 1997, 3(19) (3–4), 373–387.
  16. Portenko N.I. On some perturbations of symmetric stable processes. Probability theory and mathematical statistics. Proc. of the 7th Japan-Russia symposium, Tokyo, Japan, July 26-30, 1995. Singapore: World Scientific., 1996, 414–422.
  17. Portenko M.I. Diffusion Processes in Media with Membranes. Proceedings of the Institute of Mathematics of the Ukrainian National Academy of Sciences, 10, 1995. (in Ukrainian)