Borzdyko’s uniqueness theorems for fractal-fractional ordinary differential equations with power-law kernels and hysteresis
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.
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