کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7154686 | 1462583 | 2018 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
No nonlocality. No fractional derivative
ترجمه فارسی عنوان
بدون غیرقانونی هیچ مشتق قطعی
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کلمات کلیدی
26A3334A08Fractional derivatives and integralsMemory - حافظهNonlocality - غیرقانونی بودنFractional derivative - مشتق جزئیConformable fractional derivative - مشتق قطعه سازگارCaputo–Fabrizio fractional derivative - مشتق کاپوتو فابریزیو کسرLocal fractional derivative - مشتق کسر محلیFractional differential equations - معادلات دیفرانسیل جزئی
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی مکانیک
چکیده انگلیسی
The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small neighborhood of the considered point. Therefore differential equation, which is considered for this point and contains a finite number of integer-order derivatives, cannot describe nonlocality in space and time. This allows us to propose a principle of nonlocality for fractional derivatives. We state that if the differential equation with fractional derivative can be presented as a differential equation with a finite number of integer-order derivatives, then this fractional derivative cannot be considered as a derivative of non-integer order. This means that all results obtained for this type of fractional derivatives can be derived by using differential operators with integer orders. To illustrate the application of the nonlocality principle, we prove that the conformable fractional derivative, the M-fractional derivative, the alternative fractional derivative, the local fractional derivative and the Caputo-Fabrizio fractional derivatives with exponential kernels cannot be considered as fractional derivatives of non-integer orders.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 62, September 2018, Pages 157-163
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 62, September 2018, Pages 157-163
نویسندگان
Vasily E. Tarasov,