الفهرس 
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Abstract
The fractional calculus operators Iα and Dα, integration and differentiations αЄR+, are singular integral and differential operators. Most of the theory and applications of such operations are concerned with real-valued functions (see [23]-[35]). The concept of fractional calculus was developed by some authors (see [43] and [47] for instance). In [43], the stochastic fractional integration and differentiation are defined for the second order stochastic processes and the properties of this stochastic fractional calculus are illustrated in mean square sense, In [47], the concept of the definite integrals of fractional order for the set-valued functions are studied. Here, in chapter5, we give another generalization of the fractional calculus operators namely, fractional calculus in Banach spaces and weak topologies. Moreover, we will stablish some sufficient conditions for an integrable, continuous and weakly continuous solutions for some nonlinear functional integral equations of arbitrary orders.