Structural Obstructions and Corrections to "Existence, Uniqueness and Stability Analysis for Delay Fractional Evolution Equations with Maxima"

We examine several assertions in F. Abdeldjebbar, N. Rezoug, A. Salim and M. Benchohra, Analysis 46 (2026), 21–38, concerning delay fractional evolution equations with maxima. Several independent structural, analytic and logical obstructions are identified. First, the quantity[maxt-≤ s≤ t y(s)]is not intrinsically defined as a (Y)-valued operation on an arbitrary Banach space, so the abstract formulation and related lemmas require additional ordered structure or a separately prescribed history functional. Second, the compactness assumption imposed on the cosine family forces the underlying Banach space to be finite dimensional under the interpretation used in the original proof, conflicting with the intended infinite-dimensional PDE application. Third, the “if and only if” assertions in Theorems 21–22 are shown not to be valid as stated. A scalar Volterra example admits a unique mild solution for arbitrarily large Lipschitz parameter while the published smallness conditions fail. Further issues include missing factors in fractional-kernel estimates, unassumed regularity and monotonicity hypotheses, inconsistencies in contraction constants and exponents, missing hypotheses in later stability theorems, and several incompatibilities in the application presented in Section 5. The note provides explicit counterexamples, corrected estimates, and possible repairs to the affected statements.