On a differential equation with Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$ and application to mass-spring-damper system

Autor:	Al-Salti, Nasser, Karimov, Erkinjon, Sadarangani, Kishin
Rok vydání:	2016
Předmět:	Mathematics - Analysis of PDEs
Zdroj:	Progress in Fractional Differentiation and Applications, 2016, 2(4):257-263
Druh dokumentu:	Working Paper
DOI:	10.18576/pfda/020403
Popis:	In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$. Under some assumptions the considered equation is reduced to an integer order differential equation and solutions for different cases are obtained in explicit forms. We also prove a uniqueness of a solution of an initial value problem with a nonlinear differential equation containing the Caputo-Fabrizio derivative. Application of our result to the mass-spring-damper motion is also presented. Comment: 11 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1605.07381 Zobrazit plný text záznamu View this record from Arxiv