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

Nasser Al-Salti, Erkinjon Karimov, Kishin Sadarangani

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18 Citations (Scopus)


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 languageEnglish
Pages (from-to)257-263
Number of pages7
JournalProgress in Fractional Differentiation and Applications
Issue number4
Publication statusPublished - Oct 1 2016



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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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