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Pseudo almost automorphy of semilinear fractional differential equations in Banach spaces. (English) Zbl 1348.34029

A semilinear fractional differential equation with Riemann-Liouville derivative in a Banach space is considered. An example of fractional relaxation-oscillation equation is also given at the end. The forcing or nonlinear perturbation is of \((\mu, \nu)\)-pseudo almost automorphic type or Stepanov-like \((\mu,\nu)\)-pseudo almost automorphic type. This kind of functions are generalization of \(\mu\) pseudo almost authomorphic functions.
Reviewer: Syed Abbas (Mandi)

MSC:

34A08 Fractional ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
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