Abstract fractional integro-differential equations involving nonlocal initial conditions in α-normReport as inadecuate




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Advances in Difference Equations

, 2011:25

Nonlinear Integrodifferential Difference Equations and Related Topics

Abstract

In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-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.

Mathematics subject classification 2000

26A33, 34G10, 34G20

KeywordsCauchy problem of abstract fractional evolution equation Nonlocal initial condition Fixed point theorem Mild solution α-norm  Download fulltext PDF



Author: Rong-Nian Wang - Jun Liu - De-Han Chen

Source: https://link.springer.com/







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