Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation

  • Abderrahim Guerfi Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria.
  • Abdelouaheb Ardjouni Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria – Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria.
Keywords: Iterative fractional differential equations, fixed point theorem, existence, uniqueness, continuous dependence, Ulam stability

Abstract

In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results.

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Published
2022-04-04
How to Cite
[1]
A. Guerfi and A. Ardjouni, “Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation”, CUBO, vol. 24, no. 1, pp. 83–94, Apr. 2022.
Section
Articles