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The existence and stability results of multi-order boundary value problems involving Riemann-Liouville fractional operators

  • Received: 26 October 2022 Revised: 26 February 2023 Accepted: 07 March 2023 Published: 13 March 2023
  • MSC : 34A08, 34A12

  • In this paper, a general framework for the fractional boundary value problems is presented. The problem is created by Riemann-Liouville type two-term fractional differential equations with a fractional bi-order setup. Moreover, the boundary conditions of the suggested system are considered as mixed Riemann-Liouville integro-derivative conditions with four different orders, which it cover a variety of specific instances previously researched. Further, the provided problem's Hyers-Ulam stability and the possibility of a fixed-point approach solution are both investigated. Finally, to support our theoretical findings, an example is developed.

    Citation: Hasanen A. Hammad, Hassen Aydi, Manuel De la Sen. The existence and stability results of multi-order boundary value problems involving Riemann-Liouville fractional operators[J]. AIMS Mathematics, 2023, 8(5): 11325-11349. doi: 10.3934/math.2023574

    Related Papers:

  • In this paper, a general framework for the fractional boundary value problems is presented. The problem is created by Riemann-Liouville type two-term fractional differential equations with a fractional bi-order setup. Moreover, the boundary conditions of the suggested system are considered as mixed Riemann-Liouville integro-derivative conditions with four different orders, which it cover a variety of specific instances previously researched. Further, the provided problem's Hyers-Ulam stability and the possibility of a fixed-point approach solution are both investigated. Finally, to support our theoretical findings, an example is developed.



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