Computation of fractional integrals via functions of hypergeometric and Bessel type

Journal of Computational and Applied Mathematics

Volumn 118, Issue 1-2, 2000, Pages 223-239

  Kilbas, A A ^a   Trujillo, J J ^b  

^a BELARUSIAN STATE UNIVERSITY   (Belarus)

^b UNIVERSIDAD DE LA LAGUNA   (Spain)

Author keywords

26A33; 33C10; 33C15; Liouville and Erdelyi Kober type fractional integrals; Modified Bessel function of the third kind; Tricomi confluent hypergeometric function

Indexed keywords

EID: 0001543953     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00291-0     Document Type: Article

References (24)

1. B. Bonilla, A.A. Kilbas, M. Rivero, L. Rodríguez, J.J. Trujillo, Modified Bessel-type function and solution of differential and integral equations, Indian J. Pure Appl. Math. 31(1) (2000), in press.
2. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G. Higher Transcendental Functions, Vol. I. 1953;McGraw-Hill, New York.
3. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G. Higher Transcendental Functions, Vol. II. 1953;McGraw-Hill, New York.
4. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G. Tables of Integral Transforms, Vol. II. 1955;McGraw-Hill, New York.
5. p,μ′ , this issue, J. Comput. Appl. Math. 118 (2000) 151-168.
6. T.P. Higgins, The Rodrigues operator transform, Tables of generalized Rodrigues formulas, Boeing Science Research Laboratory Document Mathematical Note, Vol. 438, D1-82-0493, Seattle, Washington, 1965, p. 55.
7. Kratzel E. Eine Verallgemeinerung der Laplace und Meijer transformation. Wiss. Z. Friedrich-Schiller-Univ. Jena. / Thuringen 14:1965;369-381.
8. Kratzel E. Die Faltung der. L -Transformation Wiss. Z. Friedrich-Schiller-Univ. Jena. / Thuringen 14:1965;383-390.
9. Kratzel E. Bemerkungen zur Meijer-Transformation and Anwendungwn. Math. Nachr. 30:1965;327-334.
10. Lavoie J.L., Osler T.J., Tremblay R. Fractional derivatives and special functions. SIAM Rev. 18(2):1976;240-268.
11. J.L. Lavoie, R. Tremblay, T.J. Osler, Fundamental properties of fractional derivatives via Pohhammer integrals, in: Fractional Calculus and its Application, Proceedings of the International Conference, New Haven, 1974, Lecture Notes in Mathematics, Vol. 457, 1975, pp. 323-356.
12. A.V. Letnikov, New investigations about trigonometric functions, Mat. Sb. 10 (1-4) (1882) 227-312 (in Russian).
13. A.V. Letnikov, On the definite integrals which contain functions associated with hypergeometric equation, Mat. Sb. 11(3) (1884) 327-414 (in Russian).
14. A.V. Letnikov, On hyperspherical functions and on the expansion of arbitrary function in a series of hyperspherical functions, Mat. Sb. 12(2) (1885) 205-282 (in Russian).
15. A.V. Letnikov, On hyperheometric functions of higher order, Mat. Sb. 14(1) (1888) 216-222 (in Russian).
16. Miller K.S., Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equation. 1993;Wiley Interscience, New York.
17. Nishimoto K. Fractional Calculus, Integrations and Differentiations of Arbitrary Order. 1984;Descartes Press, Koriyama.
18. Oldham K.B., Spanier J. The Fractional Calculus. 1974;Academic Press, New York.
19. Osler T.J. Leibniz rule for fractional derivatives, generalized and its applcation to infinite series. SIAM J. Appl. Math. 18(3):1970;658-674.
20. Osler T.J. Taylors series generalized for fractional derivatives and applcations. SIAM J. Math. Anal. 2(1):1971;37-46.
21. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and Series, Elementary Functions, Vol. 1. 1986;Gordon and Breach, New York.
22. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and Series, Special Functions, Vol. 2. 1986;Gordon and Breach, New York.
23. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and Series, More Special Functions, Vol. 3. 1989;Gordon and Breach, New York.
24. Samko S.G., Kilbas A.A., Marichev O.I. Fractional Integrals and Derivatives, Theory and Applications. 1993;Gordon and Breach, Yverdon.