Kilbas, Anatolii Aleksandrovich

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Total publications: 24
Scientific articles: 22

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Doctor of physico-mathematical sciences (1995)
Speciality: 01.01.01; 01.01.02 (Calculus; Differential equations)
Birth date: 20.07.1948
Keywords: fractional calculus; singular integral equations; nonlinear integral equations; integral transforms with special function kernels; H-function; Mittag-Leffelr type functions; integral operators on special function spaces; partial differential equations of mixed type; differential equations of fractional order.


Firstly in world monographic literature classical and modern results in the theory of fractional calulus of function of one and several variables are presented, and applications are given to integral and differential equations and to function theory. Necessary and suficient conditions for the solvability of some classes of singular integral equations of the first kind with weak singularities and differential equations of fractional order are established, and their solutions in closed form are given. The theory of integral transforms with H-function kernels, including the boundedness, the representation, the range and the inversion, is constructed in weighted spaces of p-summable functions, and applicatuions are given to obtain the corresponding results for integral transforms with functions of hypergeometric and bessel type kernels. Compositional and asymptotic properties are investigated for the H-function, for Mittag-Leffler type functions and for functions generalizing the modified Bessel function of third kind.


Graduated from Faculty of Mathematics of Belarusian State University (BSU) in 1971 (department of mathematical analysis). Ph.D. thesis was defended in 1976. D.Sci. thesis was defended in 1995. A list of my works contains more than 220 titles. Since 1996 I and E. I. Zverovich have led the research seminar at BSU onbondary value problems and singular integral equations named by academician F. D. Gakhov.

I am a member of Editorial Bodies of international journals "Integral Transforms and Special Functions" and "Fractional Calculus and Applied Analysis".

Main publications:
  • Samko S. G., Kilbas A. A., Marichev O. I. Fractional integrals and derivatives. Theory and applications, Gordon and Breach Science Publishers, Yveron, 1993. 1012 p.
  • Kilbas A. A., Saigo M. On solution of a nonlinear Abel–Volterra integral equation // Journal of Mathematical Analysis and Applications. 1999. V. 229, no. 1. P. 41–60.
  • Glaeske H.-J., Kilbas A. A., Saigo M. Modified Bessel type integral transform and its compositions with fractional calculus operators on spaces $F_{p,\mu }$ and $F_{p,\mu}'$ // Journal of Computational and Applied Mathematics. 2000. V. 118, no. 1–2. P. 151–168.
  • Kilbas A. A., Trujillo J. J. Differential equations of fractional order: methods, results and problems - I // Applicable Analysis. 2001. V. 78, no. 1–2. P. 153–192.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. A. A. Kilbas, V. V. Lipnevich, “Orders and types of the Wright and Mittag–Leffler functions”, Tr. Inst. Mat., 17:2 (2009),  15–22  mathnet
2. A. A. Kilbas, O. V. Skoromnik, “The solution of multidimensional integral Abel type equations with the Gauss hypergeometric function in kernels over pyramidal domain”, Tr. Inst. Mat., 17:1 (2009),  71–78  mathnet  zmath
3. A. A. Kilbas, N. V. Kniaziuk, “The integral equation with the generalized Mittag–Leffler function in the kernel in the space of integrable functions”, Tr. Inst. Mat., 16:2 (2008),  49–56  mathnet  zmath
4. A. A. Kilbas, N. V. Kniaziuk, “Modified fractional integrals and derivatives in the half-axis and differential equations of fractional order in the space of integrable functions”, Tr. Inst. Mat., 15:1 (2007),  68–77  mathnet
5. A. A. Voroshilov, A. A. Kilbas, “The Cauchy problem for the diffusion-wave equation with the Caputo partial derivative”, Differ. Uravn., 42:5 (2006),  599–609  mathnet  mathscinet; Differ. Equ., 42:5 (2006), 638–649
6. A. A. Kilbas, S. A. Marzan, “Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions”, Differ. Uravn., 41:1 (2005),  82–86  mathnet  mathscinet; Differ. Equ., 41:1 (2005), 84–89
7. A. A. Kilbas, “New trends on fractional integral and differential equations”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 147:1 (2005),  72–106  mathnet
8. A. A. Kilbas, O. A. Repin, “An Analog of the Bitsadze–Samarskii Problem for a Mixed Type Equation with a Fractional Derivative”, Differ. Uravn., 39:5 (2003),  638–644  mathnet  mathscinet; Differ. Equ., 39:5 (2003), 674–680
9. Megumi Saigo, A. A. Kilbas, “The solution of a class of linear differential equations via functions of the Mittag-Leffler type”, Differ. Uravn., 36:2 (2000),  168–176  mathnet  mathscinet; Differ. Equ., 36:2 (2000), 193–202
10. A. A. Kilbas, O. A. Repin, “A problem with a shift for a parabolic-hyperbolic equation”, Differ. Uravn., 34:6 (1998),  799–805  mathnet  mathscinet; Differ. Equ., 34:6 (1998), 796–802
11. A. A. Kilbas, Megumi Saigo, “Solution in closed form of a class of linear differential equations of fractional order”, Differ. Uravn., 33:2 (1997),  195–204  mathnet  mathscinet; Differ. Equ., 33:2 (1997), 194–204
12. A. A. Kilbas, S. A. Shlapakov, “On the composition of a Bessel-type integral operator with operators of fractional integro-differentiation and the solution of differential equations”, Differ. Uravn., 30:2 (1994),  256–268  mathnet  mathscinet; Differ. Equ., 30:2 (1994), 235–246
13. S. I. Vasilets, A. A. Kilbas, “On the solution of integral equations of the first kind with weak singularities in an $n$-dimensional spherical layer”, Dokl. Akad. Nauk SSSR, 321:5 (1991),  880–884  mathnet  mathscinet  zmath; Dokl. Math., 44:3 (1992), 804–808
14. A. A. Kilbas, M. Saigo, V. A. Zhuk, “On the composition of operators of generalized fractional integration with a differential operator in axisymmetric potential theory”, Differ. Uravn., 27:9 (1991),  1640–1642  mathnet  mathscinet  zmath
15. V. S. Adamchik, A. A. Kilbas, “Asymptotics of the Laplace convolution of two Bessel functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, 4,  74–77  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:4 (1991), 73–76
16. A. A. Kilbas, “Asymptotic representations of fractional integrals”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, 1,  30–40  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 34:1 (1990), 33–45
17. A. A. Kilbas, “Asymptotic expansions of fractional integrals and of the solutions of the Euler–Poisson–Darboux equation”, Differ. Uravn., 24:10 (1988),  1764–1778  mathnet  mathscinet; Differ. Equ., 24:10 (1988), 1174–1185
18. A. A. Kilbas, S. I. Vasilets, “On the solution of a multidimensional integral equation with a logarithmic kernel with radial density”, Differ. Uravn., 23:2 (1987),  321–328  mathnet  mathscinet  zmath
19. I. N. Zabello, A. A. Kilbas, “Bounded solutions of a system of singular integral equations”, Dokl. Akad. Nauk SSSR, 284:2 (1985),  288–291  mathnet  mathscinet  zmath
20. A. A. Andreev, A. A. Kilbas, “Some associated hypergeometric functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1984, 12,  3–12  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 28:12 (1984), 1–11
21. A. A. Kilbas, “Smoothness of multidimensional operators of potential type over a bounded domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 1983, 6,  58–61  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 27:6 (1983), 73–76
22. A. A. Kilbas, “Operators of potential type with logarithmic kernels of arbitrary nonnegative orders”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, 1,  28–37  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 23:1 (1979), 22–29

23. I. V. Gaishun, M. V. Dubatovskaya, A. A. Kilbas, S. V. Rogozin, N. J. Yurchuk, “International Conference “Analytic Methods of Analysis and Differential Equations” (AMADE-99) (September 14–18, 1999, Minsk, Belarus)”, Differ. Uravn., 36:2 (2000),  284  mathnet; Differ. Equ., 36:2 (2000), 323–324
24. A. A. Kilbas, “City Seminar on boundary value problems and special integral equations held at the Lenin Belorussia State University”, Uspekhi Mat. Nauk, 33:4(202) (1978),  239–240  mathnet

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