Sign In
Register
eISSN:2278-5299

International Journal of Latest Research in Science and Technology

DOI:10.29111/ijlrst   ISRA Impact Factor:3.35,  Peer-reviewed, Open-access Journal

A News Letter Sign UP!
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

Correspondence should be addressed to :

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

Share
Download 125
View 179
Article No. 10085
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
Copyright
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

Responsive image

MNK Publication was founded in 2012 to upholder revolutionary ideas that would advance the research and practice of business and management. Today, we comply with to advance fresh thinking in latest scientific fields where we think we can make a real difference and growth now also including medical and social care, education,management and engineering.

Responsive image

We offers several opportunities for partnership and tie-up with individual, corporate and organizational level. We are working on the open access platform. Editors, authors, readers, librarians and conference organizer can work together. We are giving open opportunities to all. Our team is always willing to work and collaborate to promote open access publication.

Responsive image

Our Journals provide one of the strongest International open access platform for research communities. Our conference proceeding services provide conference organizers a privileged platform for publishing extended conference papers as journal publications. It is deliberated to disseminate scientific research and to establish long term International collaborations and partnerships with academic communities and conference organizers.