Generalized fractional integral transforms with Gauss function kernels as G-transforms

Integral Transforms and Special Functions

Volumn 13, Issue 3, 2002, Pages 285-307

  Kilbas, Anatoly A ^a   Repin, Oleg A ^b   Saigo, Megumi ^c  

^a BELARUSIAN STATE UNIVERSITY   (Belarus)

^b SAMARA STATE UNIVERSITY OF ECONOMICS   (Russian Federation)

^c FUKUOKA UNIVERSITY   (Japan)

Author keywords

Gauss hypergeometric function; Generalized fractional integral transforms; Integral transforms with Meijer's G function in the kernels; Liouville and Kober fractional integrals; Weighted space of summable functions

Indexed keywords

EID: 0036023579     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652460213516     Document Type: Article

References (28)

1. Braaksma, B.L.J. and Schuitman, A. (1976). Some classes of Watson transforms and related integral equations for generalized functions. SIAM J. Math. Anal., 7(6), 771-798.
2. Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G. (1953). Higher Transcendental Functions, Vol. 1. McGraw-Hill, New York; Reprinted in Krieger, Melbourne, Florida, 1981.
3. Grin'ko, A.P. and Kilbas, A.A. (1990). Generalized fractional integrals in weighted Hölder spaces (Russian). Dokl. Akad. Nauk BSSR, 34(6), 493-496.
4. Kilbas, A.A. and Repin, O.A. (1998). A problem with a shift for a parabolic-hyperbolic equation (Russian). Differentsial'nye Uravnneniya, 34(6), 799-805; translation in Differential Equations, 34(6), 796-802.
5. Kilbas, A.A., Repin, O.A. and Saigo, M. (1996). Solution in closed form of boundary value problem for degenerate equation of hyperbolic type. Kyungpook Math. J., 36(2), 261-273.
6. Kober, H. (1940). On fractional integrals and derivatives. Quart. J. Math. Oxford Ser., 11, 193-211.
7. Love, E.R. (1967). Some integral equations involving hypergeometric functions. Proc. Edinburgh Math. Soc., 15(2), 169-198.
8. Love, E.R. (1967). Two more hypergeometric integral equations. Proc. Cambridge Philos. Soc., 63(4), 1055-1076.
9. Luke, Y.L. (1969). The Special Functions and Their Approximations. Academic Press, New York.
10. McBride, A.C. (1974/75). Solution of hypergeometric integral equations involving generalized functions. Proc. Edinburgh Math. Soc., 2(19), 265-285.
11. Prudnikov, A.P., Brychkov, Yu.A. and Marichev, O.I. (1990). Integrals and Series. Vol. 3. More Special Functions. Gordon and Breach, New York et alibi.
12. Repin, O.A. (1992). Boundary value problems with shift for equations of hyperbolic and mixed type (Russian). Izdatel'stvo Saratovskogo Universiteta, Samarskii Filial, Samara.
13. Repin, O.A. (1994). A nonlocal boundary value problem for a degenerate hyperbolic equation (Russian). Dokl. Akad. Nauk, 335(3), 295-296; translated in Dokl. Akad. Nauk, 49(2), 319-321.
14. Repin, O.A. (1995). On a nonlocal boundary value problem for the Euler-Poisson-Darboux equation (Russian). Differentsial'nye Uravnneniya, 31(1), 171-172.
15. Repin, O.A. (1998). On the solvability of a problem with boundary condition on the characteristics for a degenerate hyperbolic equation (Russian). Differentsial'nye Uravnneniya, 34(1), 110-113; translated in Differential Equations, 34(1), 113-116.
16. Rooney, P.G. (1982-1983). On integral transformations with G-function kernels. Proc. Royal Soc. Edinburgh, Sect. A, 93, 265-297.
17. Saigo, M. (1977/78). A remark on integral operators involving the Gauss hypergeometric functions. Math. Rep. Kyushu Univ., 11, 135-143.
18. Saigo, M. (1979). A certain boundary value problem for the Euler-Darboux equation. Math. Japon., 24(4), 377-385.
19. Saigo, M. (1980). A certain boundary value problem for the Euler-Darboux equation II. Math. Japon., 25(4), 211-220.
20. Saigo, M. (1981). A certain boundary value problem for the Euler-Darboux equation III. Math. Japon., 26(1), 103-119.
21. p·μ. Math. Nachr., 147, 285-306.
22. Saigo, M. and Kilbas, A.A. (1994). Generalized fractional integrals and derivatives in Hölder spaces. Transforms Methods and Special Functions (Proc. Intern. Workshop 1995), Sofia, 12-17, August, Science Culture Techn. Publ., Singapore, pp. 282-293.
23. v,r-space. Fukuoka Univ. Sci. Rep., 30(2), 181-200.
24. Saigo, M., Repin, O.A. and Kilbas, A.A. (1996). On a non-local boundary value problem for an equation of mixed parabolic-hyperbolic type. Intern. J. Math. Stat. Sci., 5(1), 103-117.
25. Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993). Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Yverdon et alibi.
26. Saxena, R.K. and Kumbhat, R.K. (1973). A generalization of Kober operators (Hindi). Vijnana Parishad Anusandhan Patrika, 16, 31-36.
27. Saxena, R.K. and Kumbhat, R.K. (1975). Some properties of generalized Kober operators (Hindi). Vijnana Parishad Anusandhan Patrika, 18(2), 139-150.
28. Srivastava, H.M. and Saigo, M. (1987). Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation. J. Math. Anal. Appl., 121(2), 325-369.