  The principal aim of the present paper is to establish the uniqueness and
Ulam-Hyers Mittag-Leffler (UHML) stability of solutions for a new class of
multi-terms fractional time-delay differential equations in the context of the
$\Phi$-Caputo fractional derivative. To achieve this purpose, the generalized
Laplace transform method alongside facet with properties of the Mittag-Leffler
functions (M-LFs), are utilized to give a new representation formula of the
solutions for the aforementioned problem. Besides that, the uniqueness of the
solutions of the considered problem is also proved by applying the well-known
Banach contraction principle coupled with the $\Phi$-fractional Bielecki-type
norm. While the $\Phi$-fractional Gronwall type inequality and the Picard
operator (PO) technique combined with abstract Gronwall lemma are used to prove
the UHML stability results for the proposed problem. Lastly, an example is
offered to assure the validity of the obtained theoretical results.
