Doubly-weighted pseudo almost automorphic solutions for stochastic dynamic equations with Stepanov-like coefficients on time scales

Abstract

Abstract This manuscript introduces the square-mean doubly weighted pseudo almost automorphy and also square-mean doubly weighted pseudo almost automorphy in the sense of Stepanov ( S l 2 ) over time scales. We derive results for a general stochastic dynamic system on time scales which can model a stochastic cellular neural network with time shifting delays on time scales. The coefficients are considered to be doubly weighted Stepanov-like pseudo almost automorphic functions in square-mean sense which is more general than weighted pseudo almost automorphic functions. We present several new and key results such as composition theorem for such functions on time scale. These results play a crucial role in order to study qualitative properties of nonlinear differential equations. Furthermore, we study the existence of a unique solution of stochastic delay cellular neural network on time scales. These results improve and extend the previous works in this direction. At the end, a numerical example is given to illustrate the analytical findings.