Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

  • Saïd Abbas
  • Mouffak Benchohra
  • Farida Berhoun
  • Johnny Henderson
Original Paper


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.


Differential equation Left-sided mixed Hadamard integral of fractional order Caputo–Hadamard fractional derivative Existence Measure of noncompactness Fréchet space Fixed point 

Mathematics Subject Classification

26A33 34G20 



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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  • Saïd Abbas
    • 1
  • Mouffak Benchohra
    • 2
  • Farida Berhoun
    • 2
  • Johnny Henderson
    • 3
  1. 1.Laboratory of Mathematics, Geometry, Analysis, Control and ApplicationsTahar Moulay University of SaïdaSaïdaAlgeria
  2. 2.Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-AbbèsSidi Bel-AbbèsAlgeria
  3. 3.Department of MathematicsBaylor UniversityWacoUSA

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