Two Definitions of Fractional Derivative of Powers Functions
Pure and Applied Mathematics Journal
Volume 2, Issue 1, February 2013, Pages: 10-19
Received: Dec. 11, 2012; Published: Feb. 20, 2013
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Authors
Raoelina Andriambololona, Theoretical Physics Dept., Antananarivo, Madagascar; Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Rakotoson Hanitriarivo, Theoretical Physics Dept., Antananarivo, Madagascar; Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Tokiniaina Ranaivoson, Theoretical Physics Dept., Antananarivo, Madagascar; Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Roland Raboanary, Theoretical Physics Dept., Antananarivo, Madagascar; Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
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Abstract
We consider the set of powers functions defined on R_+ and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative integers, positive and negative fractional orders. Properties of linearity and commutativity are studied and the notions of semi-equality, semi-linearity and semi-commutativity are introduced. Our approach gives a unified definition of the common derivatives and integrals and their generalization.
Keywords
Gamma Function; Fractional Derivatives; Fractional Integrals; Power Functions
To cite this article
Raoelina Andriambololona, Rakotoson Hanitriarivo, Tokiniaina Ranaivoson, Roland Raboanary, Two Definitions of Fractional Derivative of Powers Functions, Pure and Applied Mathematics Journal. Vol. 2, No. 1, 2013, pp. 10-19. doi: 10.11648/j.pamj.20130201.12
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