Taiwanese Journal of Mathematics

Some Miscellaneous Properties and Applications of Certain Operators of Fractional Calculus

Shy-Der Lin and H. M. Srivastava

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Abstract

In recent years, various operators of fractional calculus (that is, calculus of integrals and derivatives of arbitrary real or complex orders) have been investigated and applied in many remarkably diverse fields. The main object of this paper is to consider some miscellaneous properties and applications which are associated with several fractional differintegral operators. We first investigate, in a systematic and unified manner, various families of series identities which emerged in connection with some of these fractional differintegral formulas. By using such operators of fractional calculus, a number of integral formulas as well as fractional differintegral formulas involving inverse hyperbolic functions are also evaluate.

Article information

Source
Taiwanese J. Math., Volume 14, Number 6 (2010), 2469-2495.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406085

Digital Object Identifier
doi:10.11650/twjm/1500406085

Mathematical Reviews number (MathSciNet)
MR2761609

Zentralblatt MATH identifier
1223.26009

Subjects
Primary: 26A33: Fractional derivatives and integrals 33B15: Gamma, beta and polygamma functions 33C05: Classical hypergeometric functions, $_2F_1$
Secondary: 33C20: Generalized hypergeometric series, $_pF_q$ 33C60: Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions)

Keywords
fractional calculus fractional differintegral operators series identities integral formulas inverse hyperbolic functions Gamma function power functions composite functions rational functions fractional differintegral formulas generalized hypergeometric functions Fox-Wright functions Gauss hypergeometric function $n$th derivative formula generalized Leibniz rule analytic functions index law linearity property principal value $F$ and $H$ functions hypergeometric reduction formulas Legendre's duplication formula incomplete Gamma function harmonic numbers exponential integrals combinatorial identity Psi (or Digamma) function

Citation

Lin, Shy-Der; Srivastava, H. M. Some Miscellaneous Properties and Applications of Certain Operators of Fractional Calculus. Taiwanese J. Math. 14 (2010), no. 6, 2469--2495. doi:10.11650/twjm/1500406085. https://projecteuclid.org/euclid.twjm/1500406085


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