This manuscript aims to study the effectiveness of two different levels of fractional orders in the frame of
Caputo-Hadamard (ℂℍ)-derivatives on a special type class of delay problem supplemented by Dirichlet boundary
conditions. The corresponding Hadamard fractional integral equation is derived for a proposed ℂℍ-fractional
pantograph system. The Banach, Schaefer, and Krasnoselskii fixed point theorems (𝔽ℙ𝕋𝑠), are used to investigate
sufficient conditions of the existence and uniqueness theorems for the proposed system. Furthermore, the Green
functions properties are investigated and used to discuss the Ulam-Hyers (𝕌ℍ)stability and its generalized by
utilizing nonlinear analysis topics. Finally, three mathematical examples are provided with numerical results and figures by using Matlab software to illustrate the validity of our findings.
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