Existence of solution for Hadamard proportional fractional integral equations by Fixed point ‎theorem

‎‎‎In this article‎, ‎using the technique of the measure of non-compactness and the Petryshyn's fixed point theorem in Banach algebra an existence theorem for some Hadamard proportional fractional integral equations is provided.‎ The study of these integral equations are important because they contain lots of particular cases of integral equations that arise in many branches of nonlinear analysis and its applications. ‎Comparing Petryshyn's fixed point theorem to Schauder and‎ ‎Darbo's fixed point theorems‎, ‎that is, it enables us to skip demonstrating closed‎, ‎convex, and compactness‎ ‎properties on the investigated operators‎. ‎‎ Finally, some examples are provided for the accuracy and efficiency of the obtained results.