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An Extension of the Fractional Gronwall Inequality

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

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Abstract

In this work, we prove a generalization of the Gronwall type inequality. This relation can be used in the qualitative analysis of the solutions to fractional differential equations with the \(\psi \)-fractional derivatives.

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Acknowledgments

R. Almeida is supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2019. A. B. Malinowska is supported by the Bialystok University of Technology grant S/WI/1/2016 and T. Odzijewicz by the Warsaw School of Economics grant KAE/S18/08/18.

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Authors and Affiliations

  1. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Ricardo Almeida

  2. Faculty of Computer Science, Bialystok University of Technology, 15-351, Białystok, Poland

    Agnieszka B. Malinowska

  3. Department of Mathematics and Mathematical Economics, Warsaw School of Economics, 02-554, Warsaw, Poland

    Tatiana Odzijewicz

Authors
  1. Ricardo Almeida
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  2. Agnieszka B. Malinowska
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  3. Tatiana Odzijewicz
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Corresponding author

Correspondence to Tatiana Odzijewicz .

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Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Almeida, R., Malinowska, A.B., Odzijewicz, T. (2020). An Extension of the Fractional Gronwall Inequality. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_2

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