SOME MISCELLANEOUS PROPERTIES AND APPLICATIONS OF CERTAIN OPERATORS OF FRACTIONAL CALCULUS

作者：Lin Shy Der; Srivastava H M^*

来源：Taiwanese Journal of Mathematics, 2010, 14(6): 2469-2495.

DOI：10.11650/twjm/1500406085

• 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
• nth 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

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 evaluated.

• 出版日期2010-12