Orthonormality and best approximation to solve non-linear fractional delay differential equations

Fazeli Ghazimahalleh, S. M.; Rabbani, Mohsen; Arab, Reza

doi:10.22075/ijnaa.2026.42339.5785

Orthonormality and best approximation to solve non-linear fractional delay differential equations

Articles in Press

Document Type : Research Paper

Authors

S. M. Fazeli Ghazimahalleh

Mohsen Rabbani

Reza Arab

Islamic Azad University,

10.22075/ijnaa.2026.42339.5785

Abstract

In this article, we present a numerical method for solving nonlinear fractional delay differential equations in Banach space based on orthonormal Legendre polynomials. We exploit the orthonormality of the basis functions to simplify the construction of the operational matrices and reduce the computational operations of the numerical procedure. Moreover, we present a technique to convert nonlinear terms to a suitable form for applying in operational matrix based on orthonormality and best approximation. As a result, the method requires fewer computational operations while maintaining an acceptable accuracy. To demonstrate the effectiveness of the proposed method we present some examples.

Keywords

Orthonormal polynomials

Fractional delay differential equations

Riemann-Liouville integral

Caputo fractional derivative

operational matrices

Subjects