Abstract fractional integro-differential equations involving nonlocal initial conditions in alpha-norm

作者：Wang Rong Nian^*; Liu Jun; Chen De Han

来源：Advances in Difference Equations, 2011, 25.

DOI：10.1186/1687-1847-2011-25

• Cauchy problem of abstract fractional evolution equation
• Nonlocal initial condition
• Fixed point theorem
• Mild solution
• alpha-norm

In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in alpha-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered.

• 出版日期2011
• 单位南昌大学