An accurate operational matrix method based on Lagrange polynomials for solving fractional-order pantograph delay and Riccati differential equations

Author:

Kumar Saurabh,Gupta Vikas,Kumar Ajay,Gómez-Aguilar J FORCID

Abstract

Abstract This paper introduces the fractional-order Lagrange polynomials approach to solve initial value problems for pantograph delay and Riccati differential equations involving fractional-order derivatives. The fractional derivative is determined as per the idea of Caputo. First, operational matrices of fractional integration with fractional-order Lagrange polynomials have been constructed using the Laplace transform. Then, we use these operational matrices and the collocation method to convert the given initial value problem to a system of algebraic equations. Subsequently, we use Newton’s iterative approach to solve the resultant system of algebraic equations. Error estimates for the function approximation also have been discussed. Finally, some numerical examples supported the theoretical findings by demonstrating the applicability and accuracy of the proposed strategy.

Publisher

IOP Publishing

Subject

Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics

Reference57 articles.

1. Fractional calculus in the transient analysis of viscoelastically damped structures;Bagley;AIAA J.,1985

2. Technical briefs;Kulish;Noise & Vibration Worldwide,2000

3. Advances in fractional calculus: theoretical developments and applications in physics and engineering;McBride;JSTOR,2007

4. Porcine dermis in uniaxial cyclic loading: sample preparation, experimental results and modeling;Ehret;Journal of Mechanics of Materials and Structures,2011

5. On the appearance of the fractional derivative in the behavior of real materials;Torvik;Journal of Applied Mechanics, Transactions ASME,1984

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3