On some abstract differential equations of fractional order with application

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Mahmoud M. El-Borai a, Khaled T. Ramadan b, M. W. Saleha, Mohamed Magdy El-Tony b


In this paper, we consider the abstract differential equation of fractional order of the form                     

we examine the existence and uniqueness of the solution of the initial value problem in a Banach Space  for the considered abstract nonlinear differential equation. We study also the correct formulation to this problem.

An application is obtained for some partial differential equations of fractional order.

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