Abstract
By means of a Laplace transform and its inverse transform, we obtain a correct equivalent integral equation for some kind of nonlocal abstract differential equations (fractional order) on the right half-axis. Based on it, the existence result is established by Knaster’s theorem, and the uniqueness of the mild solution is obtained using the Banach contraction principle.
Highlights
Today, fractional order calculus has a great many of uses in engineering, science, economy, biology, physics and other scientific disciplines
Numerous phenomena and processes in the real world are described by differential equations of fractional order
Nonlocal evolution equations of fractional order have become one of the hot research topics in the field of differential equations with fractional derivatives, which play a role in modeling physics phenomena
Summary
Fractional order calculus has a great many of uses in engineering, science, economy, biology, physics and other scientific disciplines (see [1,2,3]). A fair number of those papers investigating the mild solutions of evolution equations with fractional derivatives are concerned with bounded intervals, and conclusions on the right half-axis are still rare. Motivated by [19, 20, 31], we discuss a class of nonlocal functional differential equations of fractional order in a Banach space E
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