Borzdyko’s uniqueness theorems for fractal-fractional ordinary differential equations with power-law kernels and hysteresis
Abstract
Fractal–fractional differential equations have emerged as a powerful mathematical framework for modeling complex systems exhibiting memory effects, nonlocality, and hysteresis phenomena. This study investigates a class of fractal-fractional ordinary differential equations characterized by a power-law memory kernel and influenced by hysteresis behavior. The continuity of the function g(t,w(t)) over closed subsets of R, is used to establish the foundational results. A supporting lemma is introduced to facilitate the development of a uniqueness theorem. Drawing upon Borzdyko’s framework, we derive existence results pertinent to the targeted family of equations.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Fractional Differential Equations Solutions
Fuzzy Systems and Optimization
Publication details
- Journal / source
- An International Journal of Optimization and Control Theories & Applications (IJOCTA)
- Volume
- 16
- Issue
- 2
- Pages
- 555–555
- Publication date
- 19 January 2026