کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5775097 1413574 2017 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Non-local fractional derivatives. Discrete and continuous
ترجمه فارسی عنوان
مشتقات کسری غیر محلی. گسسته و پیوسته
کلمات کلیدی
اپراتورهای غیر محلی، مشتقات کسری گسسته، هالد برآورد می کند، نیمه گروه ها،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
We prove maximum and comparison principles for the discrete fractional derivatives in the integers. Regularity results when the space is a mesh of length h, and approximation theorems to the continuous fractional derivatives are shown. When the functions are good enough (Hölder continuous), these approximation procedures give a measure of the order of approximation. These results also allow us to prove the coincidence, for Hölder continuous functions, of the Marchaud and Grünwald-Letnikov derivatives in every point and the speed of convergence to the Grünwald-Letnikov derivative. The discrete fractional derivative will be also described as a Neumann-Dirichlet operator defined by a semi-discrete extension problem. Some operators related to the Harmonic Analysis associated to the discrete derivative will be also considered, in particular their behavior in the Lebesgue spaces ℓp(Z).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 1, 1 May 2017, Pages 734-755
نویسندگان
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