Certain operators of fractional calculus and their applications associated with logarithmic and Digamma functions
Date
2009-08-27T21:34:46Z
Authors
Tu, S-T.
Chyan, D-K.
Srivastava, H.M.
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Abstract
In the significantly vast literature on fractional calculus, one finds many systematic (and historical) accounts of its theory and applications in a number of areas including (for example) ordinary and partial differential equations, integral equations, special functions, and summation of series. The main object of the present note is to examine rather closely some recent contributions by S.-T. Tu and D.-K. Chyan [J. Fractional Calculus 7(1995), 41-46] dealing mainly with the fractional differintegrals of logarithmic functions in terms of the Psi (or Digamma) functions. Some generalizations and relevant connections with certain familiar results in the theory of fractional calculus are also given.
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Keywords
fractional calculus, ordinary and partial differential equations, integral equations, special functions, summation of series, fractional differintegrals, logarithmic functions, Psi (or Digamma) functions, differintegral operator, Riemann-Liouville fractional derivative (or integral), Weyl fractional derivative (or integral), Pochhammer symbol, Leibniz rule, multiple-valued functions, Euler-Mascheroni constant, Eulerian (Beta) integral, analytic continuation, summation formula