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

Socpus ID

84946301716 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84946301716

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