Qualitative analysis of implicit fractional differential equations involving Caputo-Hadamard derivative
Journal of Applied Mathematics and Computing, vol.72, no.8, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 72 Issue: 8
- Publication Date: 2026
- Doi Number: 10.1007/s12190-026-02872-2
- Journal Name: Journal of Applied Mathematics and Computing
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Compendex, INSPEC, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: Continuous dependence, Existence of solutions, Fixed point theorem, Fractional differential equation, Ulam-type stability
- Yıldız Technical University Affiliated: Yes
Abstract
This paper is concerned with qualitative properties of solutions to an initial value problem for nonlinear implicit fractional differential equations involving the Caputo-Hadamard derivative. Existence of solutions is obtained under sufficient conditions by means of Schauder’s fixed point theorem. A Gronwall-type inequality is then applied to derive estimates of solutions and to establish continuous dependence on the initial data, from which uniqueness follows. The Ulam-type stability is also investigated by a fixed point approach in a generalized metric space. Examples are given to illustrate the obtained results.