A Result on Solvability of Some Fractional Integro-differential Equations in Abstract Spaces


This paper concerns with a class of fractional integro-differential equations in the space of continuous functions which defined on interval \( \left[ 0,a\right] \) and take values in a Banach space E. Using a generalized Darbo fixed-point theorem associated with measure of noncompactness, the existence of solutions has been established. Also an example which shows that the main result is applicable is given.

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Correspondence to Ümit Çakan.

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Çakan, Ü. A Result on Solvability of Some Fractional Integro-differential Equations in Abstract Spaces. Bull. Iran. Math. Soc. 46, 987–1001 (2020). https://doi.org/10.1007/s41980-019-00306-3

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  • Integro-differential equations
  • Measure of noncompactness
  • Darbo fixed-point theorem
  • Fractional integral and derivative

Mathematics Subject Classification

  • 26A33
  • 34A08
  • 45M99
  • 47H08
  • 47H10