### Abstract

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.

Original language | English |
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Pages (from-to) | 257-263 |

Number of pages | 7 |

Journal | Progress in Fractional Differentiation and Applications |

Volume | 2 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 1 2016 |

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### Keywords

- Caputo-Fabrizio derivative
- Integral equation
- Mass-spring-damper system
- Nonlinear differential equation

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Progress in Fractional Differentiation and Applications*,

*2*(4), 257-263. https://doi.org/10.18576/pfda/020403

**On a differential equation with Caputo-Fabrizio fractional derivative of order 1 < b < 2 and application to mass-spring-damper system.** / Al-Salti, Nasser; Karimov, Erkinjon; Sadarangani, Kishin.

Research output: Contribution to journal › Article

*Progress in Fractional Differentiation and Applications*, vol. 2, no. 4, pp. 257-263. https://doi.org/10.18576/pfda/020403

}

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 -