Title
The Fractional Calculus And Its Role In The Synthesis Of Special Functions: Part I
Abstract
This paper is concerned with the concepts and properties of derivintegral of arbitrary order (real or complex). The relation between the Cauchy formula for repeated integrals and the Riemann-Liouville integral of integer order is demonstrated. Several general properties of the derivintegral of arbitrary order are discussed. Special emphasis is given to the product rule for arbitrary order derivintegrals. The Riemann-Liouville fractional integral R−αf and the Weyl fractional integral W−αf (α > 0) are discussed in some detail. It is shown that these integrals can be expressed as the convolution. The Mellin transforms of R−αf and W-αf are calculated. It is shown that R−αand W−αbehave like adjoint operators. Several simple examples are cited. © 1988 Taylor and Francis Group, LLC.
Publication Date
3-1-1988
Publication Title
International Journal of Mathematical Education in Science and Technology
Volume
19
Issue
2
Number of Pages
215-230
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1080/0020739880190202
Copyright Status
Unknown
Socpus ID
84946301716 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84946301716
STARS Citation
Debnath, Lokenath and Grum, William J., "The Fractional Calculus And Its Role In The Synthesis Of Special Functions: Part I" (1988). Scopus Export 1980s. 268.
https://stars.library.ucf.edu/scopus1980/268