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International Journal of Latest Research in Science and Technology

DOI:10.29111/ijlrst   ISRA Impact Factor:3.35

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Definitions of complex order integrals and complex order derivatives using operator approach

Research Paper Open Access

International Journal of Latest Research in Science and Technology Vol.1 Issue 4, pp 317-323,Year 2012

DEFINITIONS OF COMPLEX ORDER INTEGRALS AND COMPLEX ORDER DERIVATIVES USING OPERATOR APPROACH

Raoelina Andriambololona, Ranaivoson Tokiniaina,Hanitriarivo Rakotoson

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Received : 13 December 2012; Accepted : 17 December 2012 ; Published : 31 December 2012

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Abstract

For a complex number , the -order integral of a function fulfilling some conditions is defined as the action of an operator, noted , on . The definition of the operator is given firstly for the case of complex number with positive real part. Then, using the fact that the operator of one order derivative, noted , is the left hand side inverse of the operator , an -order derivative operator, noted , is also defined for complex number with positive real part. Finally, considering the relation = , the definition of the -order integral and -order derivative is extended for any complex number . An extension of the definition domain of the operators is given too.

Key Words   
Integral, derivative, complex order, operator, fractional integral, fractional derivative, gamma fu
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References
  1. S. Miller, Kenneth, “An introduction to the fractional calculus and the fractional differential equations,” Bertram Ross (Editor). Publisher: John Wiley and Sons 1st edition (1993) ISBN 0-471-58884-9
  2. B.Oldham Keith and J. Spanier “The fractional calculus. Theory and Application of differentiation and integration to arbitrary order,” (Mathematics in Science and engineering).  Publisher: Academic Press, Nov 1974, ISBN 0-12-525550-0 
  3. Raoelina Andriambololona, Rakotoson Hanitriarivo, Tokiniaina Ranaivoson, Roland Raboanary, “Two definitions of fractional derivatives of power functions,” Institut National des Sciences et Techniques Nucleaires (INSTN-Madagascar), 2012, arXiv:1204.1493
  4. Raoelina Andriambololona,“Definition of real order integrals and derivatives using operator approach,” preprint Institut National des Sciences et Techniques Nucléaires, (INSTN-Madagascar), May 2012, arXiv:1207.0409
  5. E. Artin, “The gamma function,” Holt, Rinehart and Winston, New York, 1964.
  6. S.C. Krantz “The gamma and beta functions § 13.1 in handbook of complex analysis,” Birkhauser, Boston, MA, 1999, pp.155-158.
  7. E.T Whittaker and G.N. Watson, “A course of modern analysis,” Cambridge University Press, Cambridge, 1965
  8. R. Herrmann. Fractional calculus. “An introduction for physicists,” World Scientific Publishing, Singapore, 2011.
  9. Raoelina Andriambololona,  “Algèbre linéaire et multilinéaire. Applications,” 3 Tomes. Collection LIRA, INSTN Madagascar, Antananarivo, Madagascar, 1986, Tome I pp 2-59.
To cite this article

Raoelina Andriambololona, Ranaivoson Tokiniaina,Hanitriarivo Rakotoson , " Definitions Of Complex Order Integrals And Complex Order Derivatives Using Operator Approach ", International Journal of Latest Research in Science and Technology . Vol. 1, Issue 4, pp 317-323 , 2012

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