@article{Kattan2026, 
author = {Doha A. Kattan and Hasanen A. Hammad and Najat Almutairi},
title = {Mild solutions and controllability of    (  k  ,  φ  )-Hilfer fractional delay differential equations with history-dependent operators},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {15485-15512},
keywords = {fractional derivative, Hilfer operator, fixed-point technique, history-dependent operator, measure of noncompactness, delay term},
url = {https://www.sciopen.com/article/10.3934/math.2026637},
doi = {10.3934/math.2026637},
abstract = {The objective of this work was to investigate a class of Hilfer-type fractional differential equations governed by the interaction of semigroup operators, history-dependent mechanisms, and probability density functions, with particular attention to their analytical and control properties. First, the existence of mild solutions was established through semigroup theory and fixed-point arguments tailored to fractional dynamics. We then addressed the controllability problem for the corresponding    (  k  ,  φ  )-Hilfer fractional delay differential equation, taking into account the influence of memory and delay effects induced by history-dependent operators. By combining Mönch's fixed-point theorem with the measure of noncompactness, a set of sufficient conditions for controllability was obtained. This approach not only captures the complexity of the system but also deepens the understanding of how fractional-order behavior and past-state dependence affect controllability.}
}