Existence and Stability for nonlinear variable-coefficient differential equations with non-singular kernels
by Tingting Sun, Fang Li, and Huiwen Wang
School of Mathematics, Yunnan Normal University, Kunming, 650500, P. R. China
Received on March 24, 2026, revised on April 10, 2026
Accepted on April 11, 2026
Communicated by Gaston M. N'Guérékata
| Abstract. In this work, we study an initial value problem for variable-coefficient differential equation with non-singular kernel. Firstly, we obtain existence and uniqueness of solutions for the above problem. Secondly, we obtain a stability result within the Ulam-Hyers sense of the given problem. As a special case, we obtain the corresponding conclusions with constant coefficients. An example is provided to verify the theoretical results. | |
| Keywords: | Caputo-Fabrizio derivative, variable-coefficient, Ulam-Hyers stability, constant-coefficient. |
| 2010 Mathematics Subject Classification: 26A33, 33E12, 34A08. | |
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