کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
472490 698725 2013 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Discrete direct methods in the fractional calculus of variations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
Discrete direct methods in the fractional calculus of variations
چکیده انگلیسی

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann–Liouville fractional derivative. Using the Grünwald–Letnikov definition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 66, Issue 5, September 2013, Pages 668–676
نویسندگان
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