Weighted pseudo almost automorphic solution for abstract dynamic equations under translation and non-translation time scales with shift operators and unbounded graininess

In this manuscript, we discuss the generalized almost automorphic concept of arbitrary bounded and unbounded time scales and initiate a new idea, namely the concept of changing-periodic time scales. We study weighted pseudo almost automorphic functions under the shift operator for translation and non-translation time scales. Important novel results and essential properties of such functions are established on irregular hybrid domains. The obtained results are valid for several equations defined over various time scales such as Quantum time scales, Cantor set time scales, Harmonic time scales, and so on. The idea of changing-periodic time scales presented in this paper will help in comprehension and eliminate the genuine lack that arises in the study of classical functions on time scales where the boundedness of the graininess function is required. The results are new, nontrivial, and complement the existing ones.