کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
468399 698225 2012 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Gronwall’s inequality on discrete fractional calculus
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
Gronwall’s inequality on discrete fractional calculus
چکیده انگلیسی

In this paper, we introduce discrete fractional sum equations and inequalities. We obtain the equivalence of an initial value problem for a discrete fractional equation and a discrete fractional sum equation. Then we give an explicit solution to the linear discrete fractional sum equation. This allows us to state and prove an analogue of Gronwall’s inequality on discrete fractional calculus. We employ a nabla, or backward difference; we employ the Riemann–Liouville definition of the fractional difference. As a result, we obtain Gronwall’s inequality for discrete calculus with the nabla operator. We illustrate our results with an application that gives continuous dependence of solutions of initial value problems on initial conditions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 64, Issue 10, November 2012, Pages 3193–3200
نویسندگان
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