On Erdélyi–Kober Fractional Operator and Quadratic Integral Equations in Orlicz Spaces

Mohamed M. A. Metwali () and Shami A. M. Alsallami
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Mohamed M. A. Metwali: Department of Mathematics and Computer Science, Faculty of Sciences, Damanhour University, Damanhour 22514, Egypt
Shami A. M. Alsallami: Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Mathematics, 2023, vol. 11, issue 18, 1-13

Abstract: We provide and prove some new fundamental properties of the Erdélyi–Kober ( EK ) fractional operator, including monotonicity, boundedness, acting, and continuity in both Lebesgue spaces ( L p ) and Orlicz spaces ( L φ ). We employ these properties with the concept of the measure of noncompactness ( MNC ) associated with the fixed-point hypothesis ( FPT ) in solving a quadratic integral equation of fractional order in L p , p ≥ 1 and L φ . Finally, we provide a few examples to support our findings. Our suppositions can be successfully applied to various fractional problems.

Keywords: measure of noncompactness ( MNC ); Erdélyi–Kober’s ( EK ) fractional operator; Orlicz spaces; fixed-point theorem ( FPT ) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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