Department of Mathematics, University of Tiaret, Tiaret, Algeria.
CITMAga, 15782 Santiago de Compostela, España.
Math Biosci Eng. 2022 Apr 18;19(6):6234-6251. doi: 10.3934/mbe.2022291.
In this work, we consider the problem of the existence and uniqueness of solution, and also the simple existence of solution, for implicit differential equations of arbitrary order involving Caputo-Fabrizio derivative. The main tools for this study are contraction mapping principle and Schaefer's fixed point result. We also study the stability of the equations in the sense of Ulam-Hyers and also from the perspective of Ulam-Hyers-Rassias.
在这项工作中，我们考虑了含有 Caputo-Fabrizio 导数的任意阶隐式微分方程的解的存在唯一性和简单存在性问题。这项研究的主要工具是压缩映射原理和 Schaefer 的不动点定理。我们还研究了方程在 Ulam-Hyers 意义下以及从 Ulam-Hyers-Rassias 角度的稳定性。
