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

Uniqueness and Ulam-Hyers-Mittag-Leffler stability results for the  delayed fractional multi-terms differential equation involving the  $\Phi$--Caputo fractional Derivative