Abstract
In this paper, we study the existence of mild solutions for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. The arguments are based on the Schauder fixed point theorem.
Highlights
The purpose of the present paper is to present an alternative approach to the existence of solution of fractional semilinear integro-differential equations in an arbitrary Banach space X of the form x t A t x t f t, x t t u t, s, x s ds (1)U t,t I ( I is the identity operator in X ), is a given function
We study the existence of mild solutions for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space
The arguments are based on the Schauder fixed point theorem
Summary
The purpose of the present paper is to present an alternative approach to the existence of solution of fractional semilinear integro-differential equations in an arbitrary Banach space X of the form x t A t x t f. In order to prove the existence of fixed points, we shall rely on the Schauder theorem. An application to fractional differential equations is provided to illustrate the results of this work
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
