On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation

Valizadeh, Moslem; Mahmoudi, Yaghoub; Dastmalchi Saei, Farhad

doi:10.22034/cmde.2023.58018.2444

On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation

Document Type : Research Paper

Authors

¹ Department of Mathematics, Tabriz branch, Islamic Azad University, Tabriz, Iran

² Department of Mathematics, Tabriz Branch Islamic Azad University, Tabriz, Iran

³ Department of Mathematics, Tabriz Branch,Islamic Azad University, Tabriz, Iran

10.22034/cmde.2023.58018.2444

Abstract

This paper presents the development of a series of
fractional multi-step linear finite difference methods (FLMMs)
designed to address fractional multi-delay pantograph differential
equations of order $0 < \alpha \leq 1$. These $p$-FLMMs are
constructed using fractional backward differentiation formulas of
first and second orders, thereby facilitating the numerical solution
of fractional differential equations. Notably, we employ accurate
approximations for the delayed components of the equation,
guaranteeing the retention of stability and convergence
characteristics in the proposed $p$-FLMMs. To substantiate our
theoretical findings, we offer numerical examples that corroborate
the efficacy and reliability of our approach.

Keywords

Main Subjects