Fractional order continuity and some properties about integrability and differentiability of real functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:231

Article

Bonilla, B ; Trujillo, JJ

关键词: fractional calculus;    alpha-continuity;    fractional derivative;    fractional integral;    Riemann-Liouville operator;    index rule;   

DOI  :  10.1006/jmaa.1998.6223

来源: Elsevier

【 摘 要 】

In this paper a certain function space C-alpha, 0 less than or equal to alpha less than or equal to 1, larger than the space of continuous functions, is introduced in order to study new properties and the extension of some already known results about the Riemann-Liouville fractional integral and derivative operators. Sufficient conditions for the continuity of I(a)(1-alpha)f are given. Furthermore, necessary conditions are given for the pointwise existence of fractional derivatives. The existence of a derivative of order beta, from the existence of a certain derivative of order alpha, beta < alpha, is also analyzed. (C) 1999 Academic Press.

【 授权许可】

Free