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

Authors

  • Mohammed Messous Laboratory of Informatics and Mathematics, Department of Mathematics,\\ University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria
  • Abdelouaheb Ardjouni Department of Mathematics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria; Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria

Abstract

The analysis presented in this paper commences by transforming the iterative Caputo fractional relaxation differential equation into an integral equation through the application of the Laplace and inverse Laplace transforms. Subsequently, we investigate the existence and uniqueness, as well as the Ulam stability and continuous dependence of its mild nonnegative solutions. The theorem of Schauder fixed-point is employed to establish the main theoretical results. Finally, we provide two examples to show what we have found.

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Published

2026-02-28

Issue

Vol. 33 No. 1 (2026): Nonlinear Studies

Section

Articles

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Copyright (c) 2026 Mohammed Messous, Abdelouaheb Ardjouni

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Existence, uniqueness, Ulam stability and continuous dependence of mild nonnegative solutions for an iterative fractional relaxation differential equation. (2026). Nonlinear Studies, 33(1), 21`9-234. https://www.nonlinearstudies.com/index.php/nonlinear/article/view/4152