The author applies Krasnoselskii’s fixed point theorem to prove the existence continuous solution of the system of fractional order integral equations
under the conditions of continuity and monotonicity (the are nondecreasing and the are nonincreasing). The existence of the maximal and minimal solutions has been proved when . These results generalize that of the author, A. M. A. El-Sayed and O. L. Moustafa [Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 42, No. 2, 209–220 (2002; Zbl 1033.45003)].