081bcdd5-5dfa-42d5-a307-095ff4d8aabb20210319023227676wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL1991-876310.37394/23203http://wseas.org/wseas/cms.action?id=4073220202022020201510.37394/23203.2020.15http://wseas.org/wseas/cms.action?id=23195The Asymptotic Behavior of Solutions of a Fractional Integro-differential EquationAhmad M.AhmadKing Fahd University of Petroleum & Minerals, Dhahran, SUADI ARABIAIn this paper, we study the asymptotic behavior of solutions for an initial value problem with a nonlinearfractional integro-differential equation. Most of the existing results in the literature assume the continuity of theinvolved kernel. We consider here a kernel that is not necessarily continuous, namely, the kernel of the RiemannLiouville fractional integral operator that might be singular. We determine certain sufficient conditions underwhich the solutions, in an appropriate underlying space, behave eventually like power functions. 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