Filomat 2022 Volume 36, Issue 17, Pages: 6009-6020
https://doi.org/10.2298/FIL2217009M
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On some properties of Riemann-Liouville fractional operator in Orlicz spaces and applications to quadratic integral equations
Metwali Mohamed M.A. (Department of Mathematics, Faculty of Sciences, Damanhour University, Egypt), metwali@sci.dmu.edu.eg
This article demonstrates some properties of the Riemann-Liouville (R-L)
fractional integral operator like acting, continuity, and boundedness in
Orlicz spaces Lφ. We apply these results to examine the solvability of the
quadratic integral equation of fractional order in Lφ. Because of the
distinctive continuity and boundedness conditions of the operators in Orlicz
spaces, we look for our concern in three situations when the generating
N-functions fulfill Δ′, Δ2, or Δ3-conditions. We utilize the analysis of the
measure of noncompactness with the fixed point hypothesis. Our hypothesis
can be effectively applied to various fractional problems.
Keywords: Quadratic integral equation, fractional integral operator, compactness in measure, Orlicz spaces, Δ′, Δ2, or Δ3-conditions
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