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Weighted Stepanov-like pseudoperiodicity and applications. (English) Zbl 1468.34106

Summary: By the weighted ergodic space, we propose a new class of functions called weighted Stepanov-like pseudoperiodic function and explore its properties. Furthermore, the existence and uniqueness of the weighted pseudoperiodic solution to fractional integro-differential equations and nonautonomous differential equations are investigated. Some interesting examples are presented to illustrate the main findings.

MSC:

34K37 Functional-differential equations with fractional derivatives
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K30 Functional-differential equations in abstract spaces
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