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Abstract
In this thesis we study, under certain conditions, the existence of a unique solution of the nonhomogeneous fractional order evolution equation
the nonhomogeneous fractional order evolutionary integral equation
and the nonhomogeneous fractional order evolutionary integro-differential equation
where is a closed linear operator with dense domain in the Banach space . Also we prove the continuation properties of the solution and its fractional derivative . Finally we prove the maximal regularity property of the solution and give some examples.