A coupled system of $ p $-Laplacian implicit fractional differential equations depending on boundary conditions of integral type

Dongming Nie; Usman Riaz; Sumbel Begum; Akbar Zada; Dongming Nie; Usman Riaz; Sumbel Begum; Akbar Zada

doi:10.3934/math.2023839

AIMS Mathematics

2023, Volume 8, Issue 7: 16417-16445. doi: 10.3934/math.2023839

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Research article

A coupled system of $ p $-Laplacian implicit fractional differential equations depending on boundary conditions of integral type

1.
Department of Common Courses, Anhui Xinhua University, Hefei 230088, China
2.
Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology, Peshawar, Pakistan
3.
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan

Received: 11 March 2023 Revised: 18 April 2023 Accepted: 22 April 2023 Published: 09 May 2023
MSC : 26A33, 34A08, 34B27

The objective of this article is to investigate a coupled implicit Caputo fractional $ p $-Laplacian system, depending on boundary conditions of integral type, by the substitution method. The Avery-Peterson fixed point theorem is utilized for finding at least three solutions of the proposed coupled system. Furthermore, different types of Ulam stability, i.e., Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability, are achieved. Finally, an example is provided to authenticate the theoretical result.
- $ p $-Laplacian operator,
- coupled system of fractional differential equations,
- positive solutions,
- stability in the form of Ulam
Citation: Dongming Nie, Usman Riaz, Sumbel Begum, Akbar Zada. A coupled system of $ p $-Laplacian implicit fractional differential equations depending on boundary conditions of integral type[J]. AIMS Mathematics, 2023, 8(7): 16417-16445. doi: 10.3934/math.2023839

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Abstract

The objective of this article is to investigate a coupled implicit Caputo fractional $ p $-Laplacian system, depending on boundary conditions of integral type, by the substitution method. The Avery-Peterson fixed point theorem is utilized for finding at least three solutions of the proposed coupled system. Furthermore, different types of Ulam stability, i.e., Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability, are achieved. Finally, an example is provided to authenticate the theoretical result.

References

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