Application of hat functions in solving fractional delay differential equations

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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.

Language:
Persian
Published:
Journal of Mathematical Researches, Volume:9 Issue: 4, 2024
Pages:
186 to 205
https://www.magiran.com/p2695914  
سامانه نویسندگان
  • Somayeh Nemati
    Corresponding Author (1)
    Associate Professor Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
    Nemati، Somayeh
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