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Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces

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Abstract

This paper is devoted to study the existence of solutions of a Cauchy type problem for a nonlinear fractional differential equation, via the techniques of measure of noncompactness. The investigation is based on a new fixed point result which is a generalization of the well known Darbo’s fixed point theorem. The main result is less restrictive than those given in the literature. Some illustrative examples are given.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

    Asadollah Aghajani & Ehsan Pourhadi

  2. Departamento de Análisis Matemático, Universidad de La Laguna, 38271, La Laguna, Tenerife, Spain

    Juan J. Trujillo

Authors
  1. Asadollah Aghajani
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  2. Ehsan Pourhadi
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  3. Juan J. Trujillo
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Correspondence to Asadollah Aghajani.

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Aghajani, A., Pourhadi, E. & Trujillo, J.J. Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces. fcaa 16, 962–977 (2013). https://doi.org/10.2478/s13540-013-0059-y

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