We give an existence-uniqueness result for linear and nonlinear time fractional evolution equations with singularities in corresponding norm in extended Colombeau algebra of generalized functions using fractional analog for Duhamel principle. Paper deals with some nonlinear models with singularities appearing in viscoelasticity and in anomalous processes which have met great interest among researchers who consider them as a challenge in recent years.
 R. Gorenflo, F. Mainardi, Fractional Calculus; Integral and Differential Equations of fractional order, CISM Lecture notes, In: A. Carpinteri, F. Mainardi (Ed.), Fractals and Fractional Calculus in Continuum mechanics (Springer Verlag, Wien and New York, 1997) 233
 A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, In: J. van Mill (Ed.), North-Holland Mathematics studies 204 (Elsevier, Amsterdam, Netherlands, 2006)
 I. Podlubny, Fractional Differential Equations, (Academic Press, San Diego, 1999)
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