Generalized Caputo fractional differential equations with nonlocal conditions
Abstract
This paper investigates the existence and uniqueness of solutions for fractional differential equations with nonlocal conditions. The results are derived using measure theory, Monch's fixed point theorem, and semigroup theory. An illustrative example is also presented, involving a nonlocal fractional evolution problem in $ L^2((0, \pi), \mathbb{R}) $. This example demonstrates the effect of the $ \psi $-Caputo derivative on the mild solution in comparison with the standard Caputo derivative, highlighting the influence of non-uniform time scaling and memory effects.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Fractional Differential Equations Solutions
Fuzzy Systems and Optimization
Publication details
- Journal / source
- Electronic Research Archive
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 34
- Issue
- 1
- Pages
- 196–208
- Publication date
- 1 January 2026