Advances in Difference Equations (Jan 2020)

Solvability of functional-integral equations (fractional order) using measure of noncompactness

  • Reza Arab,
  • Hemant Kumar Nashine,
  • N. H. Can,
  • Tran Thanh Binh

DOI
https://doi.org/10.1186/s13662-019-2487-4
Journal volume & issue
Vol. 2020, no. 1
pp. 1 – 13

Abstract

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Abstract We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.

Keywords