Application of hat functions in solving fractional delay differential equations

Authors
Somayeh Nemati
Zahra Rezaei Kalansara
University of Mazandaran
Abstract
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.
Keywords
fractional delay differential equations
Caputo fractional derivative
Generalized hat functions
Operational matrix of fractional integral
Delay operational matrix
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Mathematical Research
Volume 9, Issue 4 - Serial Number 27
Autumn 2023
Pages 186-205