Square-mean pseudo almost automorphic solutions of class r in the α-norm under the light of measure theory
D. Mbainadji1, I. Zabsonre2
1 Université Polytechnique de Mongo, Faculté des Sciences Fondamentales, Département de Mathématiques et Informatiques, B.P. 4377, Mongo, Tchad
2 UFR Sciences Exactes et Appliquées, Université Joseph KI-ZERBO, 03 BP 7021 Ouagadougou 03, BURKINA FASO
Received on March 4, 2024, revised version on April 10, 2025
Accepted on April 10, 2025
Communicated by Gaston M. N'Guérékata
| Abstract. 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 mapping principle and the techniques of fractional powers of an operator to obtain the required results. An example is provided for illustration. | |
| Keywords: | Measure theory, ergodicity, (µ,ν)-pseudo almost automorphic function, partial functional differential equations, stochastic processes, stochastic evolution equations. |
| 2010 Mathematics Subject Classification: 34K14, 35B15, 34G10, 60J65. | |
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