Existence and Ulam’s Stability for Conformable Fractional Differential Equations with Constant Coefficients

  • Mengmeng Li
  • JinRong WangEmail author
  • D. O’Regan


In this article, we develop a standard idea in seeking the solution of linear ODEs to derive the representation of solutions to conformable fractional linear differential equations with constant coefficients by adopting the variation of constants method. In addition, we present the existence of solutions to conformable fractional nonlinear differential equations with constant coefficients under mild conditions on the nonlinear term. Also, we transfer the concepts of Ulam’s stability for ODEs to this type of equation and give the Ulam–Hyers and Ulam–Hyers–Rassias stability results on finite time and infinite time intervals.


Conformable fractional differential equations Representation of solutions Existence Ulam–Hyers and Ulam–Hyers–Rassias stability 

Mathematics Subject Classification




The authors thank the referees for their careful reading and comments on the manuscript.


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of MathematicsGuizhou UniversityGuiyangPeople’s Republic of China
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland

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