الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The main objectives of this thesis are to study the existence of solutions in 𝐶[0,T] and 𝐿1[0,T] and some properties of this solutions for quadratic integro-differential equations. The thesis consist of two chapters and appendix as follows:We have investigated the existences of the solutions of the initial value problem of the delay quadratic functional integro-differential equation of fractional of arbitrary (fractional) orders (1) with (3) and we have proved the existence of the maximal and minimal solutions. Moreover, we have discussed the uniqueness and the continuous dependence of the solution on 𝑥0, the function 𝑔 and on the delay function 𝜙. For the continuation of problem (1) with (3) to problems (2) and (3) as α → 1, we have shown that the function 𝑓 should satisfy the Lipschitz condition.