Volume 9, Issue 4 (12-2023)                   mmr 2023, 9(4): 186-205 | Back to browse issues page

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Nemati S, Rezaei Kalansara Z. Application of hat functions in solving fractional delay differential equations. mmr 2023; 9 (4) :186-205
URL: http://mmr.khu.ac.ir/article-1-3247-en.html
1- University of Mazandaran , s.nemati@umz.ac.ir
2- University of Mazandaran
Abstract:   (400 Views)
In this paper, using a new method based on the generalized hat functions, we solve a class of fractional delay differential equations in which the fractional derivative is considered in the sense of Caputo. First, we introduce the generalized hat functions and their corresponding operational matrices. Then, in order to solve the considered problem, the existing functions are approximated using the basis functions. By employing the properties of generalized hat functions, the Caputo fractional derivative and the Riemann-Liouville fractional integral, a system of algebraic equations is obtained which by solving it, the unknown coefficients are determined. By substituting the resulting values, an approximation of the solution of the problem is obtained. In addition, the computational complexity of the resulting system is investigated. In continue, an error analysis of the method is given. Finally, the accuracy and efficiency of the proposed method are shown by presenting two examples.
Full-Text [PDF 327 kb]   (190 Downloads)    
Type of Study: Research Paper | Subject: Anal
Received: 2021/12/3 | Revised: 2024/04/7 | Accepted: 2023/05/17 | Published: 2023/12/31 | ePublished: 2023/12/31

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