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Abstract The development of fractional calculus within the framework of classical functions is now well known there are many differentstarting points for a discussion of classical fractional caculus some basic problems we sum up some basic principles of abstract differential equations in banach spaces the theory of semi groups and its relation with the construction of the solutions of evolution equations for both homogeneous and non homogeneous equations some basic definitions results and fundamental facts from functional analysis which are used in the subsequent chapters are stated in brief. |