Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Global Existence and Ulam-Hyers Stability of Ψ-Hilfer Fractional Differential Equations

  • Received : 2019.12.02
  • Accepted : 2020.04.14
  • Published : 2020.09.30
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Abstract

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.

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References

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