Fractional Order Continuity and Some Properties about Integrability and Differentiability of Real Functions

✍ Scribed by B. Bonilla; J.J. Trujillo; M. Rivero

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 72 KB
• Volume: 231
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1998.6223

✦ Synopsis

In this paper a certain function space C α , 0 ≤ α ≤ 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 1-α a f are given. Furthermore, necessary conditions are given for the pointwise existence of fractional derivatives. The existence of a derivative of order β, from the existence of a certain derivative of order α, β < α, is also analyzed.