论文信息 - Composition of erdélyi-kober fractional operators

Composition of erdélyi-kober fractional operators

In this paper we consider the Erdélyi-Kober fractional differentiation operator with nonzero lower limit of integration; and express it through an integral operator including the Gauss hypergeometric function in the Kernel. The composition of Erdélyi-Kober operators with different lower limits of integration is studied for the cases .

[1] I. N. Sneddon. The use in mathematical physics of Erdélyi-Kober operators and of some of their generalizations , 1975 .

[2] H. Kober. ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .

[3] R. A. Silverman,et al. Special functions and their applications , 1966 .

[4] D. F. Hays,et al. Table of Integrals, Series, and Products , 1966 .

[5] Megumi Saigo,et al. A remark on integral operators involving the Gauss hypergeometric functions , 1978 .

[6] B. Ross,et al. Fractional Calculus and Its Applications , 1975 .

[7] I. S. Gradshteyn,et al. Table of Integrals, Series, and Products , 1976 .

[8] V. Kiryakova. Generalized Fractional Calculus and Applications , 1993 .

[9] Yu. A. Brychkov,et al. Integrals and series , 1992 .

[10] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[11] W. Fabian. LX. Fractional calculus , 1935 .

[12] S. Kalla. Operators of fractional integration , 1980 .

[13] P. W. Karlsson,et al. Multiple Gaussian hypergeometric series , 1985 .

[14] Adam C. McBride,et al. Fractional Powers of a Class of Ordinary Differentilal Operators , 1982 .