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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohamed M. A. Metwali & Shami A. M. Alsallami, 2023. "On Erdélyi–Kober Fractional Operator and Quadratic Integral Equations in Orlicz Spaces," Mathematics, MDPI, vol. 11(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3901-:d:1239316
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    References listed on IDEAS

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    1. Ateq Alsaadi & Mieczysław Cichoń & Mohamed M. A. Metwali, 2022. "Integrable Solutions for Gripenberg-Type Equations with m -Product of Fractional Operators and Applications to Initial Value Problems," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
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