Analyzing the existence, uniqueness, and stability of solutions to boundary value problems involving a generalized fractional derivative
Abstract
This paper examines tempered fractional derivatives with respect to a kernel function, extending classical operators like Caputo and tempered derivatives. We investigate fractional differential equations (FDEs) that incorporate these generalized derivatives, focusing on the existence and uniqueness of solutions for boundary value problems. Using fixed-point theorems, we establish conditions for the existence and uniqueness of solutions. Additionally, we analyze the stability of these equations under different criteria. Our approach addresses inaccuracies in previous studies and contributes to the broader theory of fractional equations with generalized derivatives.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Nonlinear Differential Equations Analysis
Fuzzy Systems and Optimization
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 2
- Pages
- 3142–3159
- Publication date
- 1 January 2026