New aspects of Caputo-Fabrizio fractional derivative

Mohammed Al-Refai, Kamal Pal

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


In this paper, we consider classes of linear and nonlinear fractional differential equations involving the Caputo-Fabrizio fractional derivative of non-singular kernel. We transform the fractional problems to equivalent initial value problems with integer derivatives. We illustrate the obtained results by presenting two mathematical models of fractional differential equations and their equivalent initial value problems. We show that it is impossible to convert all types of linear fractional differential equations to the integer ones.The obtained results will lead to better understanding of fractional models, as the solutions of their equivalent models can be studied analytically and numerically using well-known techniques of differential equations.

Original languageEnglish
Pages (from-to)157-166
Number of pages10
JournalProgress in Fractional Differentiation and Applications
Issue number2
Publication statusPublished - 2019
Externally publishedYes


  • Caputo-Fabrizio fractional operator
  • Fractional differential equations
  • Initial value problems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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