Berikbol Torebek

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, N. Tokmagambetov, B. T. Torebek, On a non-local problem for a multi-term fractional diffusion-wave equation. arXiv:1812.01336, 24 pages 
2. M. Kirane, B. T. Torebek, Maximum principle for the fractional sequential derivatives and its application to fractional partial differential equations. Preprint. 22 pages.  
3. B. Ahmad, A. Alsaedi, M. Kirane, B. T. Torebek, Blowing-up solutions of the time-fractional Burgers, Korteweg-de Vries, Benjamin-Bona-Mahony, Rosenau and Ostrovsky type equations. arXiv:1901.09246. 22 pages. 
4. A. Kassymov, M. Kirane, B. T. Torebek, Lyapunov, Hartman-Wintner and de La Vallee Poussin-type inequalities for fractional elliptic boundary value problems. Preprint. 12 pages. 
5. M. Borikhanov, B. T. Torebek, Local and blowing-up solutions for an integro-differential diffusion equation and system. arXiv:1910.06989. 27 pages. 

Accepted papers
6. 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, 2019, doi:10.1515/jiip-2019-0031 (Published online) 
7. 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, 2019.
8. A. Alsaedi, M. Kirane, B. T. Torebek, Blow-up of smooth solutions of the time-fractional Burgers equation. Quaestiones Mathematicae, (2019).
9. M. Borikhanov, B. T. Torebek, Duhamel principle for the time-fractional diffusion equation in unbounded domain, Eurasian Mathematical Journal, (appear) 

Publications
10. 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
11. B. T. Torebek, Global Unsolvability of the Burgers Equation with Fractional Time Derivative. Differential Equations, 55:6 (2019), 867–870 
12. 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 
13. 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 
14. 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 
15. 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
16. 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 
17. 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 
18. 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 
19. 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 
20. 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 
21. N. Tokmagambetov, B. T. Torebek, Green’s formula for integro-differential operators, Journal of Mathematical Analysis and Applications, 468:1 (2018), 473–479
22. 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
23. 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 
24. 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
25. V. V. Karachik, B. T. Torebek, On the Dirichlet-Riquier Problem for Biharmonic Equations, Mathematical Notes, 102:1 (2017), 32–43
26. 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 
27. 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 
28. 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 
29. N. Tokmagambetov, B. T. Torebek, Fractional Analogue of Sturm-Liouville Operator, Documenta Mathematica, 21 (2016) , 1503–1514
30. 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
 31. 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 
32. B. Kh. Turmetov, B.T. Torebek, Modified Bavrin operators and their applications, Differential Equations, 51:2 (2015), 243–254 
33. 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 
34. 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 
35. 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
36. 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
37. 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