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Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces

Author

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  • Radko Mesiar

    (Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia
    Institute for Research and Applications of Fuzzy Modeling (IRAFM), University of Ostrava, 30. Dubna 22, 701 03 Ostrava 1, Czech Republic
    These authors contributed equally to this work.)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
    These authors contributed equally to this work.)

Abstract

We apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence and uniqueness of their solutions. Next, we compute the optimum error of the estimate. The mentioned process i.e., stabilization by a control function and finding an approximation for a pseudo functional equation is called random HUR stability. We use a fixed point technique derived from the alternative fixed point theorem (FPT) to investigate random HUR stability of the Riemann–Liouville fractional equations in MB-spaces. As an application, we introduce a class of random Wright control function and investigate existence–uniqueness and Wright stability of these equations in MB-spaces.

Suggested Citation

  • Radko Mesiar & Reza Saadati, 2021. "Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces," Mathematics, MDPI, vol. 9(14), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1602-:d:590097
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    Cited by:

    1. Anca Croitoru & Radko Mesiar & Anna Rita Sambucini & Bianca Satco, 2022. "Special Issue on Set Valued Analysis 2021," Mathematics, MDPI, vol. 10(15), pages 1-2, July.

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