Integrated semi groups and the Cauchy problem for some nonlinear fractional differential equations\n\nMahmoud M.El-Borai and Khairia El-Said El-Nadi\nm_m_elborai @ yahoo.com and [email protected]\nDepartment of Mathematics and Computer Sciences, \nFaculty of Science, Alexandria University, Egypt.\n\nAbstract. Some classes of fractional nonlinear abstract differential equations with -integrated semi groups are studied in Banach space. The existence of a unique solution of the Cauchy problem is established. An example is given.\nKey words: -integrated semi groups, nonlinear fractional differential equations, abstract Cauchy problem.\nClassifications: 47D60, 47D62 , 35 A05 , 34G20.