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Abstract: In this paper, by using the Schauder fixed point theorem, we study the existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations and obtain some new results. [Copyright &y& Elsevier]

Abstract: In this work, we present the notion of the fractional resolvent, which can be seen as a generalization of strongly continuous semigroups. We give some of its properties and apply the results to a fractional order abstract evolution equation. [Copyright &y& Elsevier]

Abstract: In this paper, by using the fixed point theory, we study the existence and uniqueness of initial value problems for nonlinear fractional differential equations and obtain a new result. [Copyright &y& Elsevier]

Abstract: We study -asymptotically -periodic solutions of the semilinear fractional equation , considered in a Banach space , where is a linear operator of sectorial type . [Copyright &y& Elsevier]

Abstract: We study almost automorphic (mild) solutions of the semilinear fractional equation , considered in a Banach space , where is a linear operator of sectorial type . We prove the existence and uniqueness of an almost automorphic mild solution assuming that is almost automorphic in for each , satisfies some Lipschitz type conditions and takes values on . [Copyright &y& Elsevier]