Abstract
In this paper, we discuss a class of fractional semilinear integrodifferential equations of mixed type with delay. Based on the theories of resolvent operators, the measure of noncompactness, and the fixed point theorems, we establish the existence and uniqueness of global mild solutions for the equations. An example is provided to illustrate the application of our main results.
Highlights
Fractional calculus can be used to describe some nonclassical phenomena in natural science and engineering applications
The initial boundary value problem for the fractional integrodifferential equations with delay has been investigated by using fixed point theorems [4, 5, 18, 20]
To the best of our knowledge, there are no results on the fractional integrodifferential equations of mixed type with delay
Summary
Fractional calculus can be used to describe some nonclassical phenomena in natural science and engineering applications. Some researchers considered sufficient conditions on the existence of mild solutions for fractional differential equations by the measure of noncompactness [4, 18, 19]. Li and Jia [25] investigated the existence of mild solutions for abstract delay fractional differential equations:. To the best of our knowledge, there are no results on the fractional integrodifferential equations of mixed type with delay. Motivated by this idea, we consider the following problem: c.
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