Affiliation:
1. College of Mathematics and Information Science, Hebei University, Baoding 071002, China
Abstract
In this paper, we investigate a class of multi-term implicit fractional differential equation with boundary conditions. The application of the Schauder fixed point theorem and the Banach fixed point theorem allows us to establish the criterion for a solution that exists for the given equation, and the solution is unique. Afterwards, we give the criteria of Ulam–Hyers stability and Ulam–Hyers–Rassias stability. Additionally, we present an example to illustrate the practical application and effectiveness of the results.
Funder
The National Natural Science Foundation of China
Reference17 articles.
1. Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier.
2. Basic theory of fractional differential equations;Lakshmikantham;Nonlinear Anal. Theory Methods Appl.,2008
3. Analysis of fractional differential equations;Diethelm;J. Math. Anal. Appl.,2002
4. Stability of Caputo fractional differential equations by Lyapunov functions;Agarwal;Appl. Math.,2015
5. Hristova, S., Tersian, S., and Terzieva, R. (2021). Lipschitz Stability in Time for Riemann–Liouville Fractional Differential Equations. Fractal Fract., 5.