Solvability of fractional integral equations by a family of measures of noncompactness in Fréchet algebra C(R+,C(J))

Amiri Kayvanloo H., Mehravaran H., SAVAŞ E., Mursaleen M.

Journal of Computational and Applied Mathematics, vol.484, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 484
  • Publication Date: 2026
  • Doi Number: 10.1016/j.cam.2026.117425
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Keywords: Fixed point theorem, Fractional differential equation, Fréchet algebras, Measures of noncompactness
  • Uşak University Affiliated: Yes

Abstract

We define the Fre´chet algebra C(R+,C(J)) and we introduce a new family of measures of noncompactness and a fixed point theorem that generalizes the Darbo's fixed point theorem in this space. By applying the technique of measures of noncompactness and new fixed point theorem, we investigate the existence of solutions of a nonlinear fractional integral equations. Some examples are provided to support our main results.