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
N1 - Publisher Copyright:
© 2016 NSP.
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
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U2 - 10.18576/pfda/020403
DO - 10.18576/pfda/020403
M3 - Article
AN - SCOPUS:85011976344
SN - 2356-9336
VL - 2
SP - 257
EP - 263
JO - Progress in Fractional Differentiation and Applications
JF - Progress in Fractional Differentiation and Applications
IS - 4
ER -