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Caputo–Fabrizio fractional differential equations with non instantaneous impulses

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Abstract

This paper deals with some existence results based on Schauder’s and Monch’s fixed point theorems and the technique of the measure of noncompactness for Cauchy problem of Caputo–Fabrizio fractional differential equations with not instantaneous impulses. Some illustrative examples are presented in the last section.

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Acknowledgements

The work of Juan J. Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014–2020 multiyear financial framework, Project MTM2016-75140-P and by Xunta de Galicia under Grant ED431C 2019/02.

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Authors and Affiliations

  1. Department of Mathematics, University of Saïda–Dr. Moulay Tahar, P.O. Box 138, EN-Nasr, 20000, Saïda, Algeria

    Saïd Abbas

  2. Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, 22000, Sidi Bel-Abbès, Algeria

    Mouffak Benchohra

  3. Departamento de Estatistica, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Juan J. Nieto

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  1. Saïd Abbas
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Correspondence to Saïd Abbas.

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Abbas, S., Benchohra, M. & Nieto, J.J. Caputo–Fabrizio fractional differential equations with non instantaneous impulses. Rend. Circ. Mat. Palermo, II. Ser 71, 131–144 (2022). https://doi.org/10.1007/s12215-020-00591-6

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