I am a current Postdoctoral Researcher at the Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University. I am a member of research group “Analysis and PDEs” of Prof. Michael Ruzhansky.

I defended my Ph.D. thesis at Al-Farabi Kazakh National University, Kazakhstan in 2017, under the supervisor of Prof. Batirkhan Turmetov and Prof. Mokhtar Kirane on *“Correctness conditions and construction of solution operators of elliptic boundary value problems in a ball”*.

**Research interests:**- Fractional Calculus and Fractional Differential Equations
- Classical and non-classical elliptic boundary value problems
- Inverse and ill-posed problems
- Extreme principle of the fractional derivatives
- Initial and boundary value problems for the PDE with fractional derivatives
- Blow-up phenomena for parabolic, hyperbolic equations with or without fractional derivatives
- Differential equations with involution
- Spectral problems for the differential and integro-differential operators

**List of Publications:**

*Preprints:*

1. M. Ruzhansky, B. T. Torebek, Van der Corput lemmas for Mittag-Leffler functions. II. α-directions, 2020, 1-19 (submitted) https://arxiv.org/abs/2005.04546

2. M. Ruzhansky, B. T. Torebek, Van der Corput lemmas for Mittag-Leffler functions, 2020, 1-32 (submitted) https://arxiv.org/abs/2002.07492

3. M. Ruzhansky, D. Serikbaev, N. Tokmagambetov, B. T. Torebek, Direct and Inverse problems for time-fractional pseudo-parabolic equations”, 1-18 (submitted) https://arxiv.org/abs/2005.08297

4. M. Kirane, B. T. Torebek, Maximum principle for space and time-space fractional partial differential equations 2020, 1-24 (submitted) https://arxiv.org/abs/2002.09314

5. M. Ruzhansky, D. Serikbaev, N. Tokmagambetov, B. T. Torebek, Direct and Inverse problems for time-fractional pseudo-parabolic equations, 2020, 1-18 (submitted) https://arxiv.org/abs/2005.08297

6. A. Kassymov, N. Tokmagambetov, B. T. Torebek, Multi-term time-fractional diffusion equation and system: mild solutions and critical exponents, Preprint, 2020, 1-17 (submitted)

7. B. Ahmad, A. Alsaedi, M. Kirane, B. T. Torebek, Blowing-up solutions of the time-fractional dispersive equations, 2020, 1-24 (submitted) https://arxiv.org/abs/1901.09246

8. A. Kassymov, M. Ruzhansky, N. Tokmagambetov, B. T. Torebek, Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for the fractional derivatives, Preprint, 2020, 1-20 (submitted)

9. M. Borikhanov, M. Kirane, B. T. Torebek, Globally unsolvability of integro-differential diffusion equations with exponential nonlinearity, Preprint, 2020, 1-20

10 M. Borikhanov, B. T. Torebek, Local existence and global nonexistence results

for the integro-differential diffusion system with nonlocal nonlinearity, Preprint, 2020, 1-18

11. A. Kassymov, M. Kirane, B. T. Torebek, Lyapunov, Hartman-Wintner and de La Vallée Poussin-type inequalities for fractional elliptic boundary value problems, 2019, Preprint, 1-14 (submitted)

12. M. Borikhanov, B. T. Torebek, Local and blowing-up solutions for an integro-differential diffusion equation and system, 2019, 1-27 (submitted) https://arxiv.org/abs/1910.06989

13. A. Kassymov, N. Tokmagambetov, B. T. Torebek, Fujita type critical exponents for time-fractional diffusion equations and systems, Preprint, 2020, 1-10 (submitted)

14. A. Kashkynbayev, D. Suragan, B. T. Torebek, “Fisher-KPP Equation on the Heisenberg group”, Preprint, 2020, 1-9.

15. M. Ruzhansky, N. Tokmagambetov, B. T. Torebek, A projection model of COVID-19 pandemic for Belgium, medRxiv, 2020, 1-10 (submitted)

*Accepted papers*

16. A. Kassymov, N. Tokmagambetov, B. T. Torebek, Nonexistence results for the hyperbolic-type equations on graded Lie groups, Bulletin of the Malaysian Mathematical Sciences Society, 2020 (Published online)

17. A. Alsaedi, M. Kirane, B. T. Torebek, Global existence and blow-up for space and time nonlocal reaction-diffusion equation, Quaestiones Mathematicae, 2020, (to appear)

https://arxiv.org/abs/1901.06632

18. M. Borikhanov, B. T. Torebek, “Duhamel principle for the time-fractional diffusion equation in unbounded domain”, Eurasian Mathematical Journal, 2019 (to appear)

*Publications*

19. M. Ruzhansky, N. Tokmagambetov, B. T. Torebek, “On a non-local problem for a multi-term fractional diffusion-wave equation”, Fractional Calculus and Applied Analysis, 23:2 (2020), 324–355

20. R. Tapdigoglu, B. T. Torebek, Global existence and blow-up of solutions of the time-fractional space-involution reaction-diffusion equation, Turkish Journal of Mathematics, 44:3 (2020), 960-969

21. M. Ruzhansky, N. Tokmagambetov, B. T. Torebek, Bitsadze-Samarskii type problem for the integro-differential diffusion-wave equation on the Heisenberg group. Integral Transforms and Special Functions, 31:1 (2020), 1-9

22. A. Alsaedi, M. Kirane, B. T. Torebek, Blow-up of smooth solutions of the time-fractional Burgers equation. Quaestiones Mathematicae, 43:2 (2020), 185-192.

23. M. Ruzhansky, N. Tokmagambetov, B. T. Torebek, Inverse source problems for positive operators. I: Hypoelliptic diffusion and subdiffusion equations. Journal of Inverse and Ill-Posed Problems, 27:6 (2019), 891-911

24. S. S. Darogomir, B. T. Torebek, Some Hermite-Hadamard type inequalities in the class of hyperbolic p-convex functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 113:4 (2019), 3413–3423

25. B. T. Torebek, Global Unsolvability of the Burgers Equation with Fractional Time Derivative. Differential Equations, 55:6 (2019), 867–870

26. M. Kirane, B. T. Torebek, Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations. Fractional Calculus and Applied Analysis, 22:2 (2019), 358–378

27. B. Ahmad, A. Alsaedi, M. Kirane, B. T. Torebek, Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals, Journal of Computational and Applied Mathematics, 353 (2019), 120–129

28. N. Al-Salti, M. Kirane, B. T. Torebek, On a class of inverse problems for a heat equation with involution perturbation. Hacettepe Journal of Mathematics and Statistics, 48:3 (2019), 669–681

29. T. Sh. Kalmenov, B. T. Torebek, A method for solving ill-posed nonlocal problem for the elliptic equation with data on the whole boundary, Journal of Pseudo-Differential Operators and Applications, 10:1 (2019), 177–185

30. T. Sh. Kalmenov, M. A. Sadybekov, B. T. Torebek, A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain, Complex Variables and Elliptic Equations, 64:3 (2019), 398–408

31. M. Kirane, B. T. Torebek, On a nonlinear problem of the breaking water waves, Bulletin of the South Ural State University, Series «Mathematical Modelling, Programming & Computer Software», 12:2 (2019), 37-46

32. N. Tokmagambetov, B. T. Torebek, Anomalous Diffusion Phenomena with Conservation Law for the Fractional Kinetic Process, Mathematical Methods in the Applied Sciences, 41:17 (2018), 8161–8170

33. M. Kirane, B. T. Torebek, A Lyapunov-type inequality for a fractional boundary value problem with Caputo-Fabrizio derivative, Journal of Mathematical Inequalities, 12:4 (2018), 1005–1012

34. M. Borikhanov, M. Kirane, B. T. Torebek, Maximum principle and its application for the nonlinear time-fractional diffusion equations with Cauchy-Dirichlet conditions, Applied Mathematics Letters, 81 (2018), 14–20

35. N. E. Tokmagambetov, B. T. Torebek, Symmetric differential operators of fractional order and their extensions, {\it Transactions of the Moscow Mathematical Society}, 2018 (2018), 177–185

36. N. Tokmagambetov, B. T. Torebek, Green’s formula for integro-differential operators, Journal of Mathematical Analysis and Applications, 468:1 (2018), 473–479

37. R. Tapdigoglu, B. T. Torebek, On a nonlinear boundary-layer problem for the fractional Blasius type equation, International Journal of Nonlinear Sciences and Numerical Simulation, 19:5 (2018), 493–498

38. B. T. Torebek, R. Tapdigoglu, Some inverse problems for the nonlocal heat equation with Caputo fractional derivative, Mathematical Methods in the Applied Sciences, 40:18 (2017), 6468–6479

39. M. Kirane, B. Samet, B.T. Torebek, Determination of an unknown source term and the temperature distribution for the sub-diffusion equation at the initial and final data, Electronic Journal of Differential Equations, 2017:257 (2017), 1–13

40. V. V. Karachik, B. T. Torebek, On the Dirichlet-Riquier Problem for Biharmonic Equations, Mathematical Notes, 102:1 (2017), 32–43

41. M. A. Sadybekov, B. T. Torebek, B. Kh. Turmetov, Representation of the Green’s function of the exterior Neumann problem for the Laplace operator, Siberian Mathematical Journal, 58:1 (2017), 153–158

42. T. Sh. Kal’menov, B. T. Torebek, On an ill-posed problem for the Laplace operator with nonlocal boundary condition, Eurasian Mathematical Journal, 8:1 (2017), 50–57

43. M. Kirane, B.T. Torebek, On a nonlocal problem for the Laplace equation in the unit ball with fractional boundary conditions, Mathematical Methods in the Applied Sciences, 39:5 (2016), 1121–1128

44. N. Tokmagambetov, B. T. Torebek, Fractional Analogue of Sturm-Liouville Operator, Documenta Mathematica, 21 (2016) , 1503–1514

45. M. A. Sadybekov, B. T. Torebek, B. Kh. Turmetov, Representation of Green’s function of the Neumann problem for a multi-dimensional ball, Complex Variables and Elliptic Equations, 61:1 (2016), 104–123

46. B. T. Torebek, B. Kh. Turmetov, Questions on solvability of exterior boundary value problems with fractional boundary conditions, Electronic Journal of Qualitative Theory of Differential Equations, 2016:25 (2016), 1–14

47. B. Kh. Turmetov, B.T. Torebek, Modified Bavrin operators and their applications, Differential Equations, 51:2 (2015), 243–254

48. B. T. Torebek, Modified Riemann–Liouville integro-differential operators in the class of harmonic functions and their applications, Ufa Mathematical Journal, 7:3 (2015), 73-83

49. M. A. Sadybekov, B. T. Torebek, B. Kh. Turmetov, On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle, Advances in Pure and Applied Mathematics, 6:3 (2015), 163-172

50. V.V. Karachik, M.A. Sadybekov, B.T. Torebek, Uniqueness of solutions to boundary-value problems for the biharmonic equation in a ball, Electronic Journal of Differential Equations, 2015:244 (2015), 1-9

51. B. Kh. Turmetov, B.T. Torebek, On solvability of some boundary value problems for a fractional analogue of the Helmholtz equation, New York Journal of Mathematics, 20:2014 (2014), 1237–1251

52. M. A. Sadybekov, B. T. Torebek, B. Kh. Turmetov, Solvability of Nonlocal Boundary-Value Problems for the Laplace Equation in the Ball, Electronic Journal of Differential Equations, 2014:157 (2014), 1-14