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Existence and Stability of Weighted Pseudo Almost Automorphic Solution of Dynamic Equation on Time Scales with Weighted Stepanov-Like (\(S^p\)) Pseudo Almost Automorphic Coefficients

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Abstract

This manuscript is dedicated to the existence and uniqueness of weighted pseudo almost automorphic solution of dynamic equation which models cellular neural network with time varying delay on time scales. The coefficients are assumed to be weighted Stepanov-like pseudo almost automorphic functions which is more general than weighted pseudo almost automorphic function. We present new result on composition theorem on time scales for the space of such functions which is important for working on nonlinear differential equations. Moreover, we obtain the exponential stability of solution using Halanay inequality. These obtained results improve and extend previous related work. Toward the last, an example with simulations for \(\mathbb {R}\) and \({\mathbb {Z}}\), which are two particular time scales, is given for the adequacy of the hypothetical outcomes.

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Acknowledgements

We are thankful to the anonymous reviewers for their insightful comments which helped us to improve the manuscript. Funding for Soniya Dhama was provided by University Grants Commission (Grant No. 2121540915).

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Correspondence to Syed Abbas.

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Dhama, S., Abbas, S. Existence and Stability of Weighted Pseudo Almost Automorphic Solution of Dynamic Equation on Time Scales with Weighted Stepanov-Like (\(S^p\)) Pseudo Almost Automorphic Coefficients. Qual. Theory Dyn. Syst. 19, 46 (2020). https://doi.org/10.1007/s12346-020-00385-2

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Keywords

  • Weighted Stepanov-like pseudo almost automorphy
  • Cellular neutral network
  • Stability
  • Time scales

Mathematics Subject Classification

  • 6H15
  • 34N05
  • 43A60