Geodesic
On some properties of Riemann-Liouville fractional operator in Orlicz spaces and applications to quadratic integral equations
Filomat, Tome 36 (2022) no. 17, p. 6009

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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 ∆′ , ∆ 2 , or ∆ 3-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.
DOI : 10.2298/FIL2217009M
Classification : 45G10, 47H30, 47N20, 46E30
Keywords: Quadratic integral equation, fractional integral operator, compactness in measure, Orlicz spaces, ∆′, ∆2, or ∆3-conditions 
Mohamed M A Metwali. On some properties of Riemann-Liouville fractional operator in Orlicz spaces and applications to quadratic integral equations. Filomat, Tome 36 (2022) no. 17, p. 6009 . doi: 10.2298/FIL2217009M
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     author = {Mohamed M A Metwali},
     title = {On some properties of {Riemann-Liouville} fractional operator in {Orlicz} spaces and applications to quadratic integral equations},
     journal = {Filomat},
     pages = {6009 },
     year = {2022},
     volume = {36},
     number = {17},
     doi = {10.2298/FIL2217009M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2217009M/}
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