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

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Abstract

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.

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Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.

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Acknowledgements

We are thankful to the handling editor and anonymous reviewers for their comments and suggestions. Second author Syed Abbas thanks for the support of Matrices SERB project No. IITM/SERB/SB/284. Third author Manuel Pinto thanks for the support of Fondecyt project 1170466. Fourth author Samuel Castillo thanks for the support of DIUBB 164408 3/R.

Funding

This study was funded by Human Resource Development Group (IITM/SERB/SB/284), Departamento de Investigaciones Científicas y Tecnológicas, Universidad de Santiago de Chile (Fondecyt project 1170466) and Universidad del Bío-Bío (DIUBB 164408 3/R).

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Authors and Affiliations

  1. Department of Mathematical Science, Rajiv Gandhi Institute of Petroleum Technology, Jais, Amethi, Uttar Pradesh, India

    Soniya Dhama

  2. School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Mandi, HP, 175005, India

    Syed Abbas

  3. Departamento de Matematicas, Facultad de Ciencias, Universidad de Chile, Santiago, Chile

    Manuel Pinto

  4. Grupo de Sistemas Dinámicos y Aplicaciones (GISDA), Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile

    Samuel Castillo

  5. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, UP, 208016, India

    Saurabh Tomar

Authors
  1. Soniya Dhama
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  2. Syed Abbas
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  3. Manuel Pinto
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  4. Samuel Castillo
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Correspondence to Syed Abbas.

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Communicated by Claudianor O. Alves.

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Dhama, S., Abbas, S., Pinto, M. et al. Weighted pseudo almost automorphic solution for abstract dynamic equations under translation and non-translation time scales with shift operators and unbounded graininess. Adv. Oper. Theory 8, 66 (2023). https://doi.org/10.1007/s43036-023-00290-w

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