Abstract
The equivalent integral equation of a new form for a class of fractional evolution equations is obtained by the method of Laplace transform, which is different from those given in the existing literature. By the monotone iterative method without the assumption of lower and upper solutions, we present some new results on the existence of positive mild solutions for the abstract fractional evolution equations on the half-line.
Highlights
1 Introduction In this paper, we are concerned with the following fractional evolution equation in the Banach space E:
One of the branches is the research on the theory about the evolution equations of fractional order, which comes from physics
Employing the monotone iterative method, without the assumption of lower and upper solutions, we present some new results on the existence of positive mild solutions for the abstract evolution equations of fractional order
Summary
1 Introduction In this paper, we are concerned with the following fractional evolution equation in the Banach space E: Where CDα + is the Caputo fractional derivative, < α < , μ > , β > , A is the infinitesimal generator of a C semigroup {T(t)}t≥ of operators on Banach E, and f : [ , +∞) × E → E satisfies certain conditions. Many of the previous papers about the existence of solutions of fractional evolution equations are only on the finite interval, and those presenting the existence results on the half-line are still few.
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