International Journal of Nonlinear Analysis and Applications

Application of a generalization of Darbo's fixed point theorem via Mizogochi-Takahashi mappings on mixed fractional integral equations involving $(k, s)$-Riemann-Liouville and Erd\'{e}lyi-Kober fractional integrals

Document Type : Research Paper

Authors

1 Department of Mathematics, Cotton University, Panbazar, Guwahati-781001, Assam, India

2 Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran

3 Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, India

4 Department of Mathematics, Azadshahr Branch, Islamic Azad University, Azadshahr, Iran

Abstract

We have established the solvability of fractional integral equations with both $(k,s)$-Riemann-Liouville and Erd'{e}lyi-Kober fractional integrals using a new generalized version of the Darbo's theorem using Mizogochi-Takahashi mappings and justify the validity of our results with the help of suitable examples.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 859-869
  • Receive Date: 27 March 2021
  • Revise Date: 10 May 2021
  • Accept Date: 29 June 2021