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


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


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.