{"product_id":"on-some-fractional-order-equations-of-evolution-von-mohamed-herzallah","title":"On Some Fractional-Order Equations of Evolution","description":"\u003cp\u003eIn this thesis we study, under certain conditions, the existence of a unique solution of the nonhomogeneous fractional order evolution equation  D^¿ u(t)=Au(t)+f(t),u(0)=u_o,t¿J=[0,T],¿¿(0,1),  the nonhomogeneous fractional order evolutionary integral equation  D^¿ u(t)=f(t)+¿_0^t¿¿ h(t-s)Au(s)ds,u(0)=u_o,¿¿(0,1),t¿J=[0,T]  and the nonhomogeneous fractional order evolutionary integro-differential equation  D^¿ u(t)=¿Au(t)+¿_0^t¿¿ k(t-s)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_¿ (t) and its fractional derivative D^¿ u_¿ (t) in the first two problems as ¿¿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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783846582800\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783846582800","offer_id":39476222820445,"sku":"9783846582800","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/c80c6796-47ca-4615-88df-f0b7b77a78d9.jpg?v=1755405990","url":"https:\/\/shop.autorenwelt.de\/en\/products\/on-some-fractional-order-equations-of-evolution-von-mohamed-herzallah","provider":"Autorenwelt Shop","version":"1.0","type":"link"}