Section 1 of the paper under review, explores the methodology and techniques of measure of weak non-compactness in order to investigate the existence of random solutions for a class of partial integral equations invoking Hadamard’s fractional integral. Interesting to note that a comprehensive text explaining the terminologies and definitions for the Pettis integrable function, mixed Pettis-Hadamard integral together with their properties are enumerated. Two fixed point theorems, called Münch and Engl’s fixed point theorems, are proved and by invoking them with the technique of measure of weak compactness, in Section 3 existence of random solution of Hadamard partial fractional integral equation (1.1) for the Pettis integrability assumption is investigated. Finally, in the last section, having considered partial random Hadamard integral equation it is established that such equations has at least one random solution.