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.
Subject:
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.
Biography
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.
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
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
2007
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
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; Differ. Equ., 42:5 (2006), 638–649
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; Differ. Equ., 41:1 (2005), 84–89
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; Differ. Equ., 39:5 (2003), 674–680
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; Differ. Equ., 36:2 (2000), 193–202
A. A. Kilbas, O. A. Repin, “A problem with a shift for a parabolic-hyperbolic equation”, Differ. Uravn., 34:6 (1998), 799–805; Differ. Equ., 34:6 (1998), 796–802
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; Differ. Equ., 33:2 (1997), 194–204
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; Differ. Equ., 30:2 (1994), 235–246
1991
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; 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
V. S. Adamchik, A. A. Kilbas, “Asymptotics of the Laplace convolution of two Bessel functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 4, 74–77; Soviet Math. (Iz. VUZ), 35:4 (1991), 73–76
1990
16.
A. A. Kilbas, “Asymptotic representations of fractional integrals”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 1, 30–40; Soviet Math. (Iz. VUZ), 34:1 (1990), 33–45
1988
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; Differ. Equ., 24:10 (1988), 1174–1185
1987
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
1985
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
1984
20.
A. A. Andreev, A. A. Kilbas, “Some associated hypergeometric functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1984, no. 12, 3–12; Soviet Math. (Iz. VUZ), 28:12 (1984), 1–11
A. A. Kilbas, “Smoothness of multidimensional operators of potential type over a bounded domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 1983, no. 6, 58–61; Soviet Math. (Iz. VUZ), 27:6 (1983), 73–76
1979
22.
A. A. Kilbas, “Operators of potential type with logarithmic kernels of arbitrary nonnegative orders”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, no. 1, 28–37; Soviet Math. (Iz. VUZ), 23:1 (1979), 22–29
2000
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; Differ. Equ., 36:2 (2000), 323–324
1978
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
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