کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
759416 1462626 2009 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fractional derivatives: Probability interpretation and frequency response of rational approximations
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Fractional derivatives: Probability interpretation and frequency response of rational approximations
چکیده انگلیسی

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 14, Issues 9–10, September–October 2009, Pages 3492–3497
نویسندگان
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