On Hyers–Ulam Stability for Fractional Differential Equations Including the New Caputo–Fabrizio Fractional Derivative

  • Yasemin BaşcıEmail author
  • Süleyman Öğrekçi
  • Adil Mısır


In this paper, we study the stability in the sense of Hyers–Ulam for the following fractional differential equations including the new Caputo–Fabrizio fractional derivative:
$$\begin{aligned} \left( ^{CF}D^{\alpha }y\right) \left( x\right) =f\left( x\right) \quad \qquad \quad \end{aligned}$$
$$\begin{aligned} \left( ^{CF}D^{\alpha } y \right) \left( x\right) -\lambda y\left( x\right) =f\left( x\right) . \end{aligned}$$
Finally, two examples are given to illustrate our results.


Fractional differential equation the new Caputo–Fabrizio fractional derivative Hyers–Ulam stability laplace transform 

Mathematics Subject Classification

26A33 34D10 



The authors would like to thank the referees for their useful comments and remarks.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yasemin Başcı
    • 1
    Email author
  • Süleyman Öğrekçi
    • 2
  • Adil Mısır
    • 3
  1. 1.Department of Mathematics, Faculty of Arts and SciencesBolu Abant Izzet Baysal UniversityBoluTurkey
  2. 2.Department of Mathematics, Faculty of Arts and SciencesAmasya UniversityAmasyaTurkey
  3. 3.Department of Mathematics, Faculty of SciencesGazi UniversityTeknikokullarTurkey

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