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Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This article deals with some existence results of solutions for a class of differential equations involving the Caputo–Hadamard fractional derivative in Fréchet spaces. These results are based on a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measure of noncompactness. We illustrate our results by an example.

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Authors and Affiliations

  1. Laboratory of Mathematics, Geometry, Analysis, Control and Applications, Tahar Moulay University of Saïda, 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 & Farida Berhoun

  3. Department of Mathematics, Baylor University, Waco, Tx, 76798-7328, USA

    Johnny Henderson

Authors
  1. Saïd Abbas
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  2. Mouffak Benchohra
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  3. Farida Berhoun
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  4. Johnny Henderson
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Correspondence to Mouffak Benchohra.

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Abbas, S., Benchohra, M., Berhoun, F. et al. Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces. RACSAM 113, 2335–2344 (2019). https://doi.org/10.1007/s13398-019-00625-4

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  • DOI: https://doi.org/10.1007/s13398-019-00625-4

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