استفاده از ماتریس عملیاتی برای حل عددی معادلات دیفرانسیل کسری

نویسندگان
فرشید میرزائی
الهام حدادیان نژاد یوسفی
دانشگاه ملایر، دانشکده علوم ریاضی و آمار، ملایر،
10.29252/mmr.2.2.65
چکیده
در این مقاله، روشی جدید بر پایۀ توابع کلاهی بهبود یافته برای حل عددی معادلات دیفرانسیل کسری غیرخطی بیان شده است. ماتریس عملیاتی انتگرال کسری به‌دست آمده و برای تبدیل معادله اصلی از دستگاه معادلات جبری استفاده شده است. این روش جواب را به‌صورت یک سری به‌سرعت هم‌گرا به‌دست می‌آورد. علاوه بر این، تجزیه و تحلیل خطای روش مورد نظر تحت چند شرط ساده ارائه شده است. سه مثال عددی برای نشان دادن کارایی و دقت روش داده شده است. مثال‌ها کارایی و کاربرد روش را نشان می‌دهند.
کلیدواژه‌ها
توابع کلاهی بهبود یافته
معادلات دیفرانسیل کسری
ماتریس عملیاتی
حسابان کسری
مشتق کاپوچو

عنوان مقاله English

Using operational matrix for numerical solution of fractional differential equations

نویسندگان English

f mirzaee
e. hadadian nejad yosofi
چکیده English

In this article, we have discussed a new application of modification of hat functions on nonlinear multi-order fractional differential equations. The operational matrix of fractional integration is derived and used to transform the main equation to a system of algebraic equations. The method provides the solution in the form of a rapidly convergent series. Furthermore, error analysis of the proposed method is provided under several mild conditions. Three numerical examples are given to show the efficiency and accuracy of the method. Illustrative examples are included to demonstrate the validity, efficiency, and applicability of the method.

کلیدواژه‌ها English

Modification of hat functions
Fractional differential equations
Operational matrices
Fractional calculus
Caputo derivative
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