Application of hat functions in solving fractional delay differential equations
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.
-
Solving Fractional Optimal Control-Affine Problems via Fractional-Order Hybrid Jacobi Functions
Zeinab Barary, Allahbakhsh Yazdani Cherati *,
Control and Optimization in Applied Mathematics, Winter-Spring 2024 -
Solving an SEIRS-α epidemic model using the third degree hat functions
Journal of Advances in Mathematical Modeling,