A class fuzzy fractional differential equation (FFDE) involving Riemann-LiouvilleH-differentiability of arbitrary orderq>1is considered. Using Krasnoselskii-Krein type conditions, Kooi type conditions, and Rogers conditions we establish the uniqueness and existence of the solution after determining the equivalent integral form of the solution.

This paper investigates the existence of positive solutions for a class of higherorder nonlinear fractional differential equations with initial conditions given for ordinary as well as fractional derivatives of the unknown function. We assume that the nonlinear term f involves also derivatives of fractional order. The results are established by converting the problem into an equivalent integral equation and applying Guo-Krasnoselskii's fixed-point theorem in cones.

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Let A be a bounded linear operator in a complex Banach space X. We show that Id X − A is a Fredholm operator provided that A has a sufficiently small polynomially measure of noncompactness. In our general framework, we note that the case of Riesz operator becomes a particular one as it is for the other results in the domain. This enable us to obtain a new characterization for the Weyl essential spectrum of a closed densely defined operators. Mathematics Subject Classification: 47A53, 47A55