کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7155011 | 1462601 | 2017 | 39 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Discrete and continuous fractional persistence problems - the positivity property and applications
ترجمه فارسی عنوان
مشکلات پایداری قطعی و دائمی - خصوصیت مثبت و کاربردها
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کلمات کلیدی
سیستم های معادلات دیفرانسیل کسری، روش های متفرقه غیر استاندارد، مثبت بودن، خطای مختلط محلی، همگرایی،
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی مکانیک
چکیده انگلیسی
In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo's derivatives) and the numerical scheme which are associated (here with discrete Grünwald-Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability of these points. We formulate explicit conditions under which a fractional system preserves positivity. We deduce also sufficient conditions to ensure order preserving. We deduce from these results a fractional persistence theorem which ensures that positivity, order preserving, equilibrium points and stability is preserved under a Caputo fractional embedding of a given differential equation. At the discrete level, the problem is more complicated. Following a strategy initiated by R. Mickens dealing with non local approximations, we define a non standard finite difference scheme for fractional differential equations based on discrete Grünwald-Letnikov derivatives, which preserves positivity unconditionally on the discretization increment. We deduce a discrete version of the fractional persistence theorem for what concerns positivity and equilibrium points. We then apply our results to study a fractional prey-predator model introduced by Javidi et al.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 44, March 2017, Pages 424-448
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 44, March 2017, Pages 424-448
نویسندگان
Jacky Cresson, Anna SzafraÅska,