Anvar Hasanov

I am currently a Leading Researcher at Institute of Mathematics, Uzbek Academy of Sciences, Tashkent, Uzbekistan. I am currently also a long-term visitor and part of Analysis & PDE group at UGent.

Academic Degree: Doctor of Philosophy, PhD in Mathematics (1982). Doctor of sciences in Physics and Mathematics (2010). Thesis Advisor: prof. M. S. Salakhitdinov.

DSC_1765

Research interests:
33C05 Classical hypergeometric functions
33C15 Confluent hypergeometric functions
33C20 Generalized hypergeometric series, pFq
33C60 Hypergeometric integrals and functions defined
33C65 Appell, Horn and Lauricella functions
35A08 Fundamental solutions
35J70 Elliptic partial differential equations of degenerate type
35L80 Hyperbolic PDE of degenerate type
35Q05 Euler-Poisson-Darboux equation and generalizations
35M10 PDE of mixed type
44A20 Transforms of special functions
44A45 Classical operational calculus
45D05 Volterra integral equations

Curriculum vitae

Publications in the reviewed journals:

  1. Maged G. Bin-SAAD, Jihad A. Younis, and Anvar Hasanov. Some mathematical properties for marginal model of poisson-gamma distribution. Kragujevac Journal of Mathematics. Vol. 47(1) (2023), Pages 105–11
  2. Maged G. Bin-Saad, Anvar Hasanov and Michael Ruzhansky.  Some properties relating to the Mittag–Leffler function of two variables. Integral Transforms and Special Functions. 2022, 33(5), pp. 400–418
  3. A. Hasanov and T. K. Yuldashev. Exact Solutions for a Partial System of Second-Order Hypergeometric Equations and Some Decomposition Formulas. Lobachevskii Journal of Mathematics, 2022, Vol. 43, No. 11, pp. 3142–3150
  4. A. Hasanov and M. Ruzhansky. Systems of differential equations of Gaussian hypergeometric functions in three variables and their linearly-independent solutions. Bulletin of the Institute of Mathematics 2022, Vol. 5, 3, pp.50-142
  5. A. Hasanov and T. K. Yuldashev. Analytic Continuation Formulas for the Hypergeometric Functions in Three Variables of Second Order. Lobachevskii Journal of Mathematics, 2022, Vol. 43, No. 5, pp. 1134–1141
  6. A. Hasanov and N. Djuraev. Exact Solutions of the Thin Beam with Degrading Hysteresis Behavior. Lobachevskii Journal of Mathematics, 2022, Vol. 43, No. 3, pp. 577–584.
  7. Anvar Hasanov, Ainur Ryskan, Junesang Choi. Decomposition Formulas for Second-Order Quadruple Gaussian Hypergeometric Series by Means of Operators H(α,β) and H(α,β). Montes Taurus J. Pure Appl. Math. 4 (3), 41–60, 2022.
  8. Anvar Hasanov, Jihad Younis and Hassen Aydi. Linearly Independent Solutions and Integral Representations for Certain Quadruple Hypergeometric Function. Journal of Function Spaces. Volume 2021, Article ID 5580131, 6 pages.
  9. Maged G. Bin-Saad, Anvar Hasanov and Jihad A. Younis. Fundamental solutions of the generalized axially symmetric Helmholtz equation. Novi Sad Journal of Mathematics. First online: 2021-03-30https://doi.org/10.30755/NSJOM.11904
  10. G. Ergashev, A. Hasanov. Appell hypergeometric functions and its application to the potential theory for a generalized bi-axially symmetric elliptic equation. Applied Analysis and Optimization. 5(1), 2021, 57-76.
  11. A. Hasanov, T.G. Ergashev. On potential theory for the generalized bi-axially symmetric elliptic equation in the plane. JMMCS. №1(109). 3-24, 2021. https://bm.kaznu.kz
  12. Anvarjon Hasanov, Tuhtasin Gulamjanovich Ergashev. New Decomposition Formulas Associated with the Lauricella Multivariable Hypergeometric Functions. Montes Taurus J. Pure Appl. Math. 3 (3), 317–326, 2021
  13. Anvar Hasanov, Jihad Younis and Hassen Aydi. On Decomposition Formulas Related to the Gaussian Hypergeometric Functions in Three Variables. Journal of Function Spaces. Volume 2021, Article ID 5538583, 6 pages. https://doi.org/10.1155/2021/5538583
  14. Anvar Hasanov and Jihad A. Younis. Application of operators $H\left( {\alpha ,\beta } \right)$ and $\bar H\left( {\alpha ,\beta } \right)$ to hypergeometric Gaussian functions in three variables. Acta Universitatis Apulensis. No. 64/2020. pp. 127-136.
  15. A.S. Berdyshev, A. Hasanov, A.R. Ryskan. Decomposition formulas for some quadruple hypergeometric series. Bulletin of the Karaganda University. Mathematics series. № 4(100)/2020. рр. 43-54. DOI 10.31489/2020M4/43-54.
    https://mathematics-vestnik.ksu.kz/2020-100-4
  16. Anvar Hasanov and Jihad Younis. Decomposition formulas for some hypergeometric functions in three variables. East-West J. of Mathematics: Vol. 22, No 2 (2020) pp. 133-140.
    http://eastwestmath.org/index.php/ewm/issue/archive
  17. T.G. Ergashev, A. Hasanov. Holmgren problem for elliptic equation with singular coefficients. Вестник КРАУНЦ. Физ.-мат. науки. 2020. Т. 32. № 3. C. 179-195.
  18. A. S. Berdyshev, A. Hasanov, and Zh. A. Abdiramanov. Solution of Cauchy Problem for the Generalized Gellerstedt Equation. Lobachevski Journal of Mathematics, 2020, Vol. 41, No. 9, pp. 1762–1771.
  19. A. Hasanov and M. Ruzhansky. Hypergeometric Expansions of Solutions of the Degenerating Model Parabolic Equations of the Third Order. Lobachevskii Journal of Mathematics, 2020, Vol. 41, No. 1, pp. 27–31.
  20. M. Ruzhansky and A. Hasanov. Self-similar Solutions of Some Model Degenerate Partial Differential Equations of the Second, Third and Fourth Order. Lobachevskii Journal of Mathematics, 2020, Vol. 41, No. 6, pp. 1103–1114. https://rdcu.be/b5H6a
  21. A.S. Berdyshev, A. Hasanov, A.R. Ryskan. Solution of the Neumann problem for one four-dimensional elliptic equation. Eurasian mathematical journal. Vol.11, Number 2 (2020), 93 – 97.
  22. Srivastava H.M., Hasanov A., Ergashev T.G. A family of potentials for elliptic equations with one singular coefficient and their applications. Mathematical Methods in Applied Sciences. 2020. Vol.43, Issue 10. Pages 6181-6199. DOI:10.1002/mma.6365
    Anvar Hasanov and Junesang Choi. Note on Euler-Bernoulli Equation. Sohag J. Math. 7, No. 2, 33-36, 2020.
  23. A. Hasanov, A. S. Berdyshev and A. R. Ryskan. Fundamental solutions for a class of four-dimensional degenerate elliptic equation. Complex variables and elliptic equations. 65 (4), 2020, pp. 632-647.
    https://doi.org/10.1080/17476933.2019.1606803
  24. Berdyshev A.S., Hasanov A. Ergashev T.G. Double-layer potentials for generalized bi-axially symmetric Helmholtz equation II. Complex variables and elliptic equations. 65, (2), 2020, pp.316-332. https://doi.org/10.1080/17476933.2019.1583219
  25. Hasanov, A. S. Berdyshev and A. R. Ryskan. Fundamental solutions for a class of four-dimensional degenerate elliptic equation. Complex variables and elliptic equations. https://doi.org/10.1080/17476933.2019.1606803
  26. Berdyshev A.S., Hasanov A. Ergashev T.G. Double-layer potentials for generalized bi-axially symmetric Helmholtz equation II. Complex variables and elliptic equations. https:/doi.org/10.1080/17476933.2019.1583219
  27. Hasanov Anvarjon, Ergashev T.G. Solutions of PDE systems for Kamp´e de F´eriet type functions. Bulletin of the Institute of Mathematics. 2018,3, pp.23-28
  28. Хасанов А., Бердышев А. Задачи на собственные значения для одного класса вырождающегося дифференциальных уравнений третьего порядка составного типа. Бюллетень института математики. 4, 2018, 1-5.
  29. Maged G. Bin-Saad, Anvar Hasanov and Mamasali Turaev. Decomposition Formulas of Kampe´ de Fe´riets Double Hypergeometric Functions. Theory Appl., Vol. 34, No. 3 (2018), pp. 275-292
  30. Hasanov A., Maged G. Bin-Saad, Berdyshev A. Solutions of PDE systems for Appell-type functions. Uzbek Mathematical Journal, 2018, 2 , pp.50-62.
  31. Anvar Hasanov, Maged G. Bin Saad, Ainur Ryskan. Some properties of Horn type second order double hypergeometric series. Bulletin KRASEC. Physical and Mathematical Sciences. № 1(21). C. 32-47, 2018.
  32. Ergashev T.G., Hasanov A. Fundamental solutions of the bi-axially symmetric Helmholtz equation. Uzbek Mathematical Journal, 2018, No1, pp.55-64.
  33. Anvar Hasanov, Maged G. Bin-Saad and Rakhila B. Seilkhanova. Applications of symbolic operators to the Kampé de Fériets double hypergeometric series. Palestine Journal of Mathematics. Vol. 7(1) (2018), 191-201.
  34. Anvar Hasanov, Maged G. Bin Saad, Rakhila B. Seilkhanova. Integrated Representations of Euler- Type for Functions Related to Kampe’ de Fe’riet Function of the Fourth Order(II). International Journal of Pure and Applied Mathematical Technologies; Vol. 2016.1.2; pp. 10-17.
  35. Anvar Hasanov, Rakhila B. Seilkhanova and Roza D. Seilova, Linearly independent solutions of the system of hypergeometric Exton function X12. Contemporary Analysis and Applied Mathematics. Vol.3, No.2, 279-282, 2015. DOI: 10.18532/caam.02474
  36. Rakhila B. Seilkhanova, Anvar H. Hasanov; Particular solutions of  generalized Euler-Poisson-Darboux equation, Electron. J. Diff. Equ., Vol. 2015 (2015), No. 09, pp. 1-10. http://ejde.math.txstate.edu/
  37. H. M. Srivastava, Anvar Hasanov and Junesang Choi. Double-Layer Potentials for a Generalized Bi-Axially Symmetric Helmholtz Equation. Sohag Journal of Mathematics An International Journal. 2, No. 1, 1-10 (2015)
  38. Anvar Hasanov, Maged G. Bin Saad, Rakhila B. Seilkhanova. Integral Representations of Euler Type for Kampe de Feriet Functions of the Fourth Order. Ganita Sandesh, V. 28, No 1 and 2, 2014, pp. 5-12.
  39. Maged G. Bin-Saad and Anvar Hasanov. Linear Independent Solutions and Operational Representations for Hypergeometric Functions of Four Variables. Chinese Journal of Mathematics. Volume 2014, pp. 1-6. Article ID 273064, 6 pages. http://dx.doi.org/10.1155/2014/273064
  40. M.S. Salakhitdinov and A. Hasanov. The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation. Eurasian Mathematical Journal, Volume 3, Number 4(2012), 99 – 110.
  41. Junesang Choi, Anvar Hasanov and Mamasali Turaev. Integral Representations for Srivastava’s Hypergeometric Functions . Honam Mathematical journal. 34 (4), 2012, 473-482.
  42. Junesang Choi, Anvar Hasanov and Mamasali Turaev. Serendipitous Functional Relations Deducible from Certain Generalized Triple Hypergeometric Functions. Kyungpook Math. J. 52(2012), 109-136
  43. Junesang Choi, Anvar Hasanov and Mamasali Turaev, Integral Representations for Srivastava’s Hypergeometric Functions. Journal of the Korea Society of Mathematical Education. 19 (2), 2012, 137-145.
  44. Junesang Choi, Anvar Hasanov and Mamasali Turaev, Certain Integral Representations of Euler type for the Exton Function . Commun. Korean Math. Soc. 27 (2012), No. 2, pp. 257-264.