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Some New Weakly Singular Integral Inequalities with Applications to Differential Equations in Frame of Tempered χ -Fractional Derivatives

Author

Listed:
  • Omar Kahouli

    (Department of Electronics Engineering, Applied College, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia)

  • Djalal Boucenna

    (Laboratory of Physical Chemistry and Biology of Materials, Higher Normal School of Technological Education (ENSET), Skikda 21000, Algeria)

  • Abdellatif Ben Makhlouf

    (Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia)

  • Ymnah Alruwaily

    (Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia)

Abstract

In this study, we develop some novel Integral Inequalities (InIs) with weakly singular singularities that expand some commonly known ones. Utilizing tempered χ -Fractional Differential Equations (FDEs), many applications for FDEs in the context of Caputo have been developed.

Suggested Citation

  • Omar Kahouli & Djalal Boucenna & Abdellatif Ben Makhlouf & Ymnah Alruwaily, 2022. "Some New Weakly Singular Integral Inequalities with Applications to Differential Equations in Frame of Tempered χ -Fractional Derivatives," Mathematics, MDPI, vol. 10(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3792-:d:942569
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    References listed on IDEAS

    as
    1. M. Abu-Shady & Mohammed K. A. Kaabar, 2021. "A Generalized Definition of the Fractional Derivative with Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, October.
    2. Abdellatif Ben Makhlouf & Djalal Boucenna & A.M. Nagy & Lassaad Mchiri & Ching-Feng Wen, 2022. "Some Weakly Singular Integral Inequalities and Their Applications to Tempered Fractional Differential Equations," Journal of Mathematics, Hindawi, vol. 2022, pages 1-9, April.
    Full references (including those not matched with items on IDEAS)

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