Journals Information
Universal Journal of Engineering Science(CEASE PUBLICATION) Vol. 3(4), pp. 53 - 63
DOI: 10.13189/ujes.2015.030401
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The Physical and Geometrical Interpretation of Fractional Order Derivatives
Ali Karci *
Department of Computer Engineering, Inonu University, Turkey
ABSTRACT
The fractional order derivative is a famous subject and it has been studied about three centuries. There are not any studies on the physical and geometrical interpretation of fractional order derivative. The aim of this study is to interpret the geometrical meaning of the fractional order derivatives of any function. We used a new definition for fractional order derivative to interpret it. At this aim, simple and easily understandable subjects distance, velocity and acceleration were used to depict the experimental results and interpretations. The important contribution of this paper is that when the order of fractional order derivative approaches to 1, the result of derivative process approaches to classical derivative and operator is linear; otherwise, the result of derivative process is different from classical derivative and applied operator is non-linear.
KEYWORDS
Fractional Calculus, Fractional Order Derivatives, Mathematical Analysis
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ali Karci , "The Physical and Geometrical Interpretation of Fractional Order Derivatives," Universal Journal of Engineering Science(CEASE PUBLICATION), Vol. 3, No. 4, pp. 53 - 63, 2015. DOI: 10.13189/ujes.2015.030401.
(b). APA Format:
Ali Karci (2015). The Physical and Geometrical Interpretation of Fractional Order Derivatives. Universal Journal of Engineering Science(CEASE PUBLICATION), 3(4), 53 - 63. DOI: 10.13189/ujes.2015.030401.