Abstract In this paper, we discuss the existence of a unique solution and Ulam–Hyers–Mittag-Leffler (UHML) stability for a nonlinear Hammerstein-type ψ -Hilfer delay differential equation of fractional order ( ψ -HFDDE) in the configuration of several variable time-dependent delays. Our study is based on fixed-point methodology. The results established in this work are novel and enhance the literature on the topic. We also present examples to illustrate the application of the obtained results. The findings of this paper provide new contributions to the qualitative theory of Hilfer fractional delay differential equations.
Tunҫ et al. (Thu,) studied this question.