TY - JOUR

T1 - On a differential equation with Caputo-Fabrizio fractional derivative of order 1 < b < 2 and application to mass-spring-damper system

AU - Al-Salti, Nasser

AU - Karimov, Erkinjon

AU - Sadarangani, Kishin

PY - 2016/10/1

Y1 - 2016/10/1

N2 - In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order 1 < b < 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.

AB - In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order 1 < b < 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.

KW - Caputo-Fabrizio derivative

KW - Integral equation

KW - Mass-spring-damper system

KW - Nonlinear differential equation

UR - http://www.scopus.com/inward/record.url?scp=85011976344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011976344&partnerID=8YFLogxK

U2 - 10.18576/pfda/020403

DO - 10.18576/pfda/020403

M3 - Article

AN - SCOPUS:85011976344

VL - 2

SP - 257

EP - 263

JO - Progress in Fractional Differentiation and Applications

JF - Progress in Fractional Differentiation and Applications

SN - 2356-9336

IS - 4

ER -