Definitions of Real Order Integrals and Derivatives Using Operator Approach
Pure and Applied Mathematics Journal
Volume 2, Issue 1, February 2013, Pages: 1-9
Received: Dec. 11, 2012; Published: Feb. 20, 2013
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Raoelina Andriambololona, Theoretical Physics Dept., Antananarivo, Madagascar, Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Boite Postale 4279, Antananarivo 101, Madagascar
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The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^sand D^k are given and demonstrated. The method is based on the properties of Euler’s gamma and beta functions.
Gamma Functions; Beta Functions; Integrals; Derivatives; Arbitrary Orders; Operators
To cite this article
Raoelina Andriambololona, Definitions of Real Order Integrals and Derivatives Using Operator Approach, Pure and Applied Mathematics Journal. Vol. 2, No. 1, 2013, pp. 1-9. doi: 10.11648/j.pamj.20130201.11
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