Semilinear fractional differential equations with infinite delay and non-instantaneous impulses

  • Mouffak BenchohraEmail author
  • Sara Litimein
  • Juan J. Nieto


In this article, we study the existence of mild solutions for a new class of impulsive semilinear fractional differential equations with infinite delay and non-instantaneous impulses in Banach spaces. The new results are obtained using suitable fixed point theorems and the technique of measures of noncompactness. An example is also given to illustrate the obtained theory.


Fractional differential equations infinite delay almost sectorial operators resolvent of operators non-instantaneous impulse conditions 

Mathematics Subject Classification

26A33 34A08 34A37 34K37 



The work of J. J. Nieto has been partially supported by the Ministerio de Economia y Competitividad of Spain, Agencia Estatal de Investigación under Grant MTM201675140-P, and XUNTA de Galicia under Grant GRC2015-004, and and co-financed by the European Community fund FEDER.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mouffak Benchohra
    • 1
    Email author
  • Sara Litimein
    • 1
  • Juan J. Nieto
    • 2
  1. 1.Laboratory of MathematicsDjillali Liabes University of Sidi Bel-AbbèsSidi Bel-AbbèsAlgeria
  2. 2.Departamento de Estatistica, Análise Matemático e Optimización, Instituto de MatemáticasUniversidade de Santiago de CompostelaSantiago de CompostelaSpain

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