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
Highlights
Let (A, D(A)) be the infinitesimal generator of a compact analytic semigroup of bounded linear operators {T(t)}t≥0 on a real Banach space (X, ||·||) and 0 Î r(A)
The present paper concerns the study of the Cauchy problem for abstract fractional integro-differential equation involving nonlocal initial condition cDβt u(t)
In the past several years theorems about existence, uniqueness and stability of Cauchy problem for abstract evolution equations with nonlocal initial conditions have been studied by many authors, see for instance [19,20,21,22,23,24,25,26,27,28] and references therein
Summary
Let (A, D(A)) be the infinitesimal generator of a compact analytic semigroup of bounded linear operators {T(t)}t≥0 on a real Banach space (X, ||·||) and 0 Î r(A). The existence of mild solutions for fractional differential equations with nonlocal initial conditions in a-norm using the contraction mapping principle and the Schauder’s fixed point theorem have been investigated in [16].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
