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Analysis study on multi-order $ \varrho $-Hilfer fractional pantograph implicit differential equation on unbounded domains

  • Received: 14 February 2023 Revised: 10 May 2023 Accepted: 17 May 2023 Published: 31 May 2023
  • MSC : 34A08, 34B10

  • In this paper, we investigate a multi-order $ \varrho $-Hilfer fractional pantograph implicit differential equation on unbounded domains $ (a, \infty), a\geq 0 $. The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers ($ \mathcal UH $), Ulam-Hyers-Rassias ($ \mathcal UHR $) and semi-Ulam-Hyers-Rassias (s-$ \mathcal UHR $) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results.

    Citation: Sabri T. M. Thabet, Sa'ud Al-Sa'di, Imed Kedim, Ava Sh. Rafeeq, Shahram Rezapour. Analysis study on multi-order $ \varrho $-Hilfer fractional pantograph implicit differential equation on unbounded domains[J]. AIMS Mathematics, 2023, 8(8): 18455-18473. doi: 10.3934/math.2023938

    Related Papers:

  • In this paper, we investigate a multi-order $ \varrho $-Hilfer fractional pantograph implicit differential equation on unbounded domains $ (a, \infty), a\geq 0 $. The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers ($ \mathcal UH $), Ulam-Hyers-Rassias ($ \mathcal UHR $) and semi-Ulam-Hyers-Rassias (s-$ \mathcal UHR $) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results.



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