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Application of measure of noncompactness to Volterra equations of convolution type. (English) Zbl 1355.45005

Summary: Sufficient conditions for the existence of at least one solution of a nonlinear integral equation with a general kernel are established. The existence result is proved in \(C([0,T],E)\), where \(E\) denotes an arbitrary Banach space. We use the Darbo-Sadovskii fixed point theorem and techniques of measure of noncompactness. We extend and generalize results obtained by other authors in the context of fractional differential equations. One example illustrates the theoretical results.

MSC:

45G10 Other nonlinear integral equations
45D05 Volterra integral equations
45N05 Abstract integral equations, integral equations in abstract spaces
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
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