کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6420517 1631798 2015 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A general form of the generalized Taylor's formula with some applications
ترجمه فارسی عنوان
فرم کلی فرمول تعمیم یافته تیلور با برخی از برنامه های کاربردی
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی


- In this article, a new general form of fractional power series is introduced.
- Some results of classical power series are circulated and proved to this new form.
- A new general form of the generalized Taylor's formula is also obtained.
- Applications including fractional power series solutions for FDEs are analyzed.
- Results reveal that, the new expansion is effective for formulating the solutions.

In this article, a new general form of fractional power series is introduced in the sense of the Caputo fractional derivative. Using this approach some results of the classical power series are circulated and proved to this fractional power series, whilst a new general form of the generalized Taylor's formula is also obtained. Some applications including fractional power series solutions for higher-order linear fractional differential equations subject to given nonhomogeneous initial conditions are provided and analyzed to guarantee and to confirm the performance of the proposed results. The results reveal that the new fractional expansion is very effective, straightforward, and powerful for formulating the exact solutions in the form of a rapidly convergent series with easily computable components.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 256, 1 April 2015, Pages 851-859
نویسندگان
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