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Multisummability of Formal Solutions for a Family of Generalized Singularly Perturbed Moment Differential Equations

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Abstract

The notion of moment differentiation is extended to the set of generalized multisums of formal power series via an appropriate integral representation and accurate estimates of the moment derivatives. The main result is applied to characterize generalized multisummability of the formal solution to a family of singularly perturbed moment differential equations in the complex domain, broadening widely the range of singularly perturbed functional equations to be considered in practice, such as singularly perturbed differential equations and singularly perturbed fractional differential equations.

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Funding

The first author is supported by the project PID2019-105621GB-I00 of Ministerio de Ciencia e Innovación, Spain. and by Dirección General de Investigación e Innovación, Consejería de Educación e Investigación of Comunidad de Madrid (Spain), and Universidad de Alcalá under grant CM/JIN/2019-010, Proyectos de I+D para Jóvenes Investigadores, Univ. de Alcalá 2019.

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Authors and Affiliations

  1. Universidad de Alcalá, Departamento de Física y Matemáticas, Ap. de Correos 20, 28871, Alcalá de Henares, Madrid, Spain

    Alberto Lastra

  2. Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszyński University, Wóycickiego 1/3, 01-938, Warszawa, Poland

    Sławomir Michalik & Maria Suwińska

Authors
  1. Alberto Lastra
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  2. Sławomir Michalik
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  3. Maria Suwińska
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All authors contributed equally and significantly in this paper and typed, read, and approved the final manuscript. All authors have made substantial contributions to the conception, design of the work, have drafted the work and substantively revised it. All authors have approved the submitted version.

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Correspondence to Alberto Lastra.

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Lastra, A., Michalik, S. & Suwińska, M. Multisummability of Formal Solutions for a Family of Generalized Singularly Perturbed Moment Differential Equations. Results Math 78, 49 (2023). https://doi.org/10.1007/s00025-022-01828-9

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