Square-mean pseudo almost automorphic Solutions of class r in the α-norm under The light of measure theory

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Résumé

The main objective of this work is to study the existence and uniqueness of the square-mean (μ, ν)-pseudo almost automorphic solution of class r in the α-norm for a stochastic partial functional differential equation. For this purpose, we use the Banach contraction principle and the techniques of fractional powers of an operator to obtain the required results. An illustrative example is provided.

Mots-clés

(μ, ν)-pseudo almost automorphic functions, ergodicity, measure theory, partial functional differential equations, stochastic evolution equations, stochastic processes.