الفهرس 
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Abstract
Fractional differential equations(differential equations of Fractional orders) are singular integro-differential equations.The main aim of this thesis is to establish sufficient conditions for obtaining a monotonic solution of the initial value problem.The thesis consists of three chapters,first chapter contains three sections.In the firs one,we briefly trace the historical development of the fractional calculus.We also give some preliminaries and known results that will be needed in the subsequent investigations.In the second section,we introduce the definitions of weak and strong measures of noncompactness such as Kuratowski.