Title
On Some FractionalOrder Equations of Evolution,Used
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In this thesis we study, under certain conditions, the existence of a unique solution of the nonhomogeneous fractional order evolution equation D^a u(t)=Au(t)+f(t),u(0)=u_o,t?J=[0,T],a?(0,1), the nonhomogeneous fractional order evolutionary integral equation D^a u(t)=f(t)+?_0^t h(ts)Au(s)ds,u(0)=u_o,a?(0,1),t?J=[0,T] and the nonhomogeneous fractional order evolutionary integrodifferential equation D^ u(t)=?Au(t)+?_0^t k(ts)Au(s)ds+f(t), u(0)=x,u'(0)=y,?(1,2),?=0, where A is a closed linear operator with dense domain D(A)=X_A in the Banach space X. Also we prove the continuation properties of the solution u_a (t) and its fractional derivative D^a u_a (t) in the first two problems as a?1^ and in the third problem we prove the continuation properties of the solution u_ (t) and its fractional drerivative D^ u_ (t) as ?1^+ and as ?2^. Finally we prove the maximal regularity property of the solution of each problem and give some examples of the three problems.
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