Shishkina, Elina Leonidovna

Total publications: 40 (40)
in MathSciNet: 24 (24)
in zbMATH: 18 (18)
in Web of Science: 19 (19)
in Scopus: 22 (22)
Cited articles: 27
Citations in Math-Net.Ru: 23
Citations in Web of Science: 63
Citations in Scopus: 130
Presentations: 4

Number of views:
This page:2031
Abstract pages:1168
Full texts:319
Shishkina, Elina Leonidovna
Associate professor
Doctor of physico-mathematical sciences (2019)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 26.11.1980
E-mail: ,
Keywords: potential type operators, fractional differentiation, weighted singular integrals, besselian operator, weight class of functions, fractional derivatives, fractional integrals.
UDC: 517.954, 517.958, 517.968, 517.983.34
MSC: 44 A


Differential equations with singularities and of fractional order, potential theory, differential equations in probability theory, fractional calculus, special functions


Graduated from the Department Mathematics of Voronezh State University (VSU) in 1953. The M.Sc. thesis was supervised by prof. O. M. Penkin. In 2004?06, taught in the Department of the Higher Mathematics of the Voronezh State Technological Academy (VSTA). Simultaneously, was a postgraduate student under supervision by prof. L. N. Lyakhov (2004?06). Defended the Ph.D. thesis in 2006. Since August 2006, taught first in "Quality Control and Machine-Building Technology Department" VSTA, since February 2008 in the mathematical department of the Voronezh State Forestry Engineering Academy. Simultaneously, since 2007 have taught in the Department of the Differential Equations of the VSU. Gave many talks on mathematical seminars and conferences in Russia and abroad.

Main publications:
  1. Lyakhov L. N., Shishkina E. L., “Generalized Riesz B-Potentials of the Mixed Type”, Doklady Mathematics, 73:1 (2006), 42–45  crossref  mathscinet  zmath; Original Russian Text: L. N. Lyakhov, E. L. Shishkina, Doklady Akademii Nauk, 406:3 (2006), 303–307  mathscinet  zmath
  2. Shishkina E. L., “Weighting Distribution $r^\lambda$”, Proceeding of Voronezh State University Series: Phisics, Mathematics, 2006, № 1, 215–221
  3. Lyakhov L. N., Shishkina E. L., “General B-Hypersingular Integrals with Homogeneous Characteristic”, Doklady Mathematics, 75:1 (2007), 39–43  crossref  mathscinet; Original Russian Text: L. N. Lyakhov, E. L. Shishkina, Doklady Akademii Nauk, 412:2 (2007), 162–166  mathscinet
  4. Sitnik S.M., Shishkina E.L., “On fractional powers of Bessel operators on half-axes”, Siberian Electronic Mathematical Reports, 2018, № 15, 1–10
  5. Shishkina E.L., Sitnik S.M., “General form of the Euler–Poisson–Darboux equation and application of the transmutation method”, Electronic Journal of Differential Equations, 2017, № 177, 1–20

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |

1. D. K. Durdiev, E. L. Shishkina, S. M. Sitnik, “Fractional powers of Bessel operator and its numerical calculation”, Chelyab. fiz.-matem. zhurn., 6:2 (2021), 172–189  mathnet  crossref;

2. E. L. Shishkina, “General Euler–Poisson–Darboux equation and hyperbolic $B$-potentials”, Partial differential equations, CMFD, 65, no. 2, PFUR, M., 2019, 157–338  mathnet  crossref
3. E. L. Shishkina, S. M. Sitnik, “A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type”, Mathematics, 7:12, 1216 (2019), 1-21  crossref  isi (cited: 4)
4. E. L. Shishkina, “The Dirichlet problem for an elliptic singular equation”, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2019, 1-10  crossref  isi (cited: 1)  scopus (cited: 1)
5. E. L. Shishkina, “Generalized divergent theorem and second Green identity of $B-$elliptic and $B-$hyperbolic operators”, Applied Mathematics & Physics, 51:4 (2019), 506–513  mathnet  crossref

6. E. L. Shishkina, “Properties of Mixed Hyperbolic B–Potential”, Progress in Fractional Differentiation and Applications, 4:2 (2018), 83-98  crossref  scopus (cited: 4)
7. E. L. Shishkina, “Singular Cauchy problem for the general Euler-Poisson-Darboux equation”, Open Mathematics, 16:1 (2018), 23–31 (Published online)  crossref  mathscinet  zmath  isi (cited: 4)  elib  scopus (cited: 6)
8. E. L. Shishkina, “Generalized Euler-Poisson-Darboux equation and singular Klein–Gordon equation”, Journal of Physics: Conference Series, 973:1 (2018), 1-20  crossref  mathscinet  isi  elib  scopus (cited: 5)
9. S. M. Sitnik, E. L. Shishkina, “On fractional powers of the Bessel operator on semiaxis”, Sib. Èlektron. Mat. Izv., 15:1 (2018), 1-10, arXiv:  mathnet  crossref  mathscinet  zmath  isi  scopus
10. E. L. Shishkina, M. Karabacak, “Singular Cauchy problem for generalized homogeneous Euler-Poisson-Darboux equation”, Matematicheskie zametki SVFU, 25:2 (2018), 85-96  mathnet  crossref  zmath  elib
11. A. V. Kuznetsov, E. L. Shishkina, S. M. Sitnik, “Probabilistic Properties of Near-Optimal Trajectories of an Agent Moving Over a Lattice”, Journal of Optimization Theory and Applications, 2018, 1-17 (Published online)  crossref  isi  scopus (cited: 1)
12. A. Fitouhi, I. Jebabli, E. L. Shishkina, S. M. Sitnik, “Applications of the integral transforms composition method to wave-type singular differential equations and index shift transmutations”, Electronic Journal of Differential Equations, 2018:130 (2018), 1-27, arXiv:  mathscinet  zmath  isi (cited: 2)  scopus (cited: 11)
13. V. V. Kravchenko, E. L. Shishkina, S. M. Torba, “On a Series Representation for Integral Kernels of Transmutation Operators for Perturbed Bessel Equations”, Math. Notes, 104:4 (2018), 530–544  mathnet  crossref  crossref  mathscinet  isi (cited: 5)  elib  scopus (cited: 7)
14. E. L. Shishkina, “Solution of the singular Cauchy problem for a general inhomogeneous Euler–Poisson–Darboux equation”, Carpathian Journal of Mathematics, 34:2 (2018) , 255- 267 pp.  crossref  mathscinet  zmath
15. I. P. Polovinkin, E. L. Shishkina, S. M. Sitnik, “Space of images of the mixed Riesz hyperbolic B-potential and analytic continuation”, Journal of Inverse and Ill-posed Problems, 2018, 10.1515/jiip-2017-0112 (Published online) , 23 pp.  crossref  mathscinet  isi  scopus

16. D. S. Donchev, S. M. Sitnik, E. L. Shishkina, “On refinements of neo-classical inequality and its applications to stochastic differential equations and Brownian motion”, Chelyab. Fiz.-Mat. Zh., 2:3 (2017), 257–265  mathnet  mathscinet  elib
17. E. L. Shishkina, “Inversion of the mixed Riesz hyperbolic B-potentials”, International Journal of Applied Mathematics, 30:6 (2017), 487-500  crossref  mathscinet  elib  scopus (cited: 6)
18. E. L. Shishkina, S. M. Sitnik, “General form of the Euler-Poisson-Darboux equation and application of the transmutation method”, Electron. J. Differential Equations, 2017, 177, 1-20, arXiv: arXiv:1707.04733  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 17)
19. E. L. Shishkina, S. M. Sitnik, “On fractional powers of Bessel operators”, Journal of Inequalities and Special Functions, 8:1 (2017), 49-67, arXiv: arXiv:1703.02232  mathscinet  isi (cited: 10)  elib
20. E. L. Shishkina, “Vesovye obobschënnye funktsii, otvechayuschie kvadratichnoi forme s kompleksnymi koeffitsientami”, Chelyabinskii fiziko-matematicheskii zhurnal, 2:1 (2017), 88-98  mathnet (cited: 3)  mathscinet  elib
21. D. S. Donchev, S. M. Sitnik., E. L. Shishkina, “Ob obobschenii binominalnoi teoremy, voznikayuschem v teorii differentsialnykh uravnenii”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika., 49:27 (276) (2017), 19-25  elib
22. S. M. Sitnik, E. L. Shishkina, “Drobnye stepeni operatora Besselya na poluosi i ikh svoistva”, Nekotorye aktualnye problemy sovremennoi matematiki i matematicheskogo obrazovaniya Materialy nauchnoi konferentsii, Rossiiskii gosudarstvennyi pedagogicheskii universitet im. A.I. Gertsena, Sankt-Peterburg, 2017, 144-150  elib

23. L. N. Lyakhov, E. L. Shishkina, “Weighted mixed spherical means and singular ultrahyperbolic equation”, Analysis: International mathematical journal of analysis and its applications, 36:2 (2016), 65-70  crossref  mathscinet  zmath  elib  scopus (cited: 2)
24. E. L. Shishkina, “On weighted generalized functions associated with quadratic forms”, Probl. Anal. Issues Anal., 5 (23):2 (2016), 52-68, arXiv: 1612.07907  mathnet (cited: 2)  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 2)
25. S. M. Sitnik, E. L. Shishkina, “On an identity for the iterated weighted spherical mean and its applications 13 (2016), 849–860”, Sib. Èlektron. Mat. Izv., 13 (2016), 849–860  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
26. E. L. Shishkina, “On the boundedness of hyperbolic Riesz B-potential”, Lithuanian Mathematical Journal, 56:4 (2016), 540–551  crossref  mathscinet  zmath  isi (cited: 5)  elib  scopus (cited: 9)
27. L. N. Lyakhov, I. P. Polovinkin, E. L. Shishkina, “Accompanying Distributions of Singular Differential Operators”, Journal of Mathematical Sciences, 219:2 (2016), 184–189  crossref  mathscinet  zmath  elib  scopus (cited: 1)
28. E. L. Shishkina, “O svoistvakh odnogo usrednyayuschego yadra v vesovom klasse Lebega”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika., 42:6 (227) (2016), 12-19  elib
29. E. L. Shishkina, “Integralnoe predstavlenie yadra operatora, approksimiruyuschego obratnyi operator dlya giperbolicheskogo V-potentsiala Rissa”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 21:2 (2016), 450-458  crossref  elib
30. O. P. Barabash, E. L. Shishkina, “Reshenie obschego uravneniya Eilera–Puassona–Darbu, soderzhaschee operator Besselya po vsem peremennym”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki., 21:6 (2016), 2146-2151  crossref  elib
31. E. L. Shishkina, “On weighted generalized functions associated with quadratic forms”, Probl. Anal. Issues Anal., 5(23):2 (2016), 52–68  mathnet (cited: 2)  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 2)
32. E. L. Shishkina, “About properties of the averaging kernel in the Lebesgue weighted class”, Applied Mathematics & Physics, 42:6 (2016), 12–19  mathnet

33. L. N. Lyakhov, I. P. Polovinkin, E. L. Shishkina, “On a Kipriyanov problem for a singular ultrahyperbolic equation”, Differential Equations, 50:4 (2014), 513-525  crossref  mathscinet  zmath  isi (cited: 10)  elib  scopus (cited: 17)
34. L. N. Lyakhov, I. P. Polovinkin, E. L. Shishkina, “Formulas for the solution of the Cauchy problem for a singular wave equation with Bessel time operator”, Doklady Mathematics, 90:3 (2014), 737-742  crossref  mathscinet  zmath  isi (cited: 8)  elib  scopus (cited: 11)

35. E. L. Shishkina, “Equality for iterated weighted spherical means generated by generalized translation”, Some current problems in modern mathematics and education in mathematics (St. Petersburg), Izdat. RGPU im. A. I. Gertsena, 2013, 143-145  mathscinet

36. E. L. Shishkina, “Inversion of integral of B-potential type with density from Φγ”, Journal of Mathematical Sciences, 160:1 (2009), 95-102  crossref  mathscinet  zmath  elib  scopus (cited: 6)
37. L. N. Lyakhov, E. L. Shishkina, “Inversion of general Riesz B-potentials with homogeneous characteristic in weight classes of functions”, Doklady Mathematics, 79:3 (2009), 377–381  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 1)

38. L. N. Lyakhov, E. L. Shishkina, “General B-hypersingular integrals with homogeneous characteristic”, Doklady Mathematics, 75:1 (2007), 39-43  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 6)

39. L. N. Lyakhov, E. L. Shishkina, “Generalized Riesz B-potentials of the mixed type”, Doklady Mathematics, 73:1 (2006), 42-45  crossref  mathscinet  zmath  isi (cited: 4)  elib  scopus (cited: 8)
40. E. L. Shishkina, “Obobschennaya vesovaya funktsiya r^\lambda”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2006, no. 1, 215-221  zmath  elib

Presentations in Math-Net.Ru
1. Метод композиционных интегральных преобразований для сингулярных дифференциальных уравнений с оператором Бесселя и его дробными степенями
E. L. Shishkina
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
October 25, 2018 11:00
2. "Метод композиционных интегральных преобразований для сингулярных дифференциальных уравнений с оператором Бесселя и его дробными степенями"
E. L. Shishkina
Seminar on analytic theory of differential equations
October 24, 2018 14:30
3. Обращение гиперболических В-потенциалов Рисса
E. L. Shishkina
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
February 14, 2018 16:00   
4. The ratio of Asgeirsson-Kipriyanov for the general ultra-hyperbolic equations
L. N. Lyakhov, I. P. Polovinkin, E. L. Shishkina
International Conference on Differential Equations and Dynamical Systems
July 5, 2014 12:20

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