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On the existence of continuous solutions for a singular system of non-linear fractional differential equations. (English) Zbl 1153.26004

The author applies Krasnoselskii’s fixed point theorem to prove the existence continuous solution of the system of fractional order integral equations

x i (t)=h i (t)+λ i I α i [f i (x(t))+g i (x(t))],t[0,1],α i (0,1),1in

under the conditions of continuity and monotonicity (the f i are nondecreasing and the g i are nonincreasing). The existence of the maximal and minimal solutions has been proved when g i (x)=c. 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)].

26A33Fractional derivatives and integrals (real functions)
35A35Theoretical approximation to solutions of PDE