Study of Sturm-Liouville boundary value problems with $ {p} $ -Laplacian by using generalized form of fractional order derivative

Abdelatif Boutiara; Mohammed S. Abdo; Mohammed A. Almalahi; Kamal Shah; Bahaaeldin Abdalla; Thabet Abdeljawad; Abdelatif Boutiara; Mohammed S. Abdo; Mohammed A. Almalahi; Kamal Shah; Bahaaeldin Abdalla; Thabet Abdeljawad

doi:10.3934/math.20221011

AIMS Mathematics

2022, Volume 7, Issue 10: 18360-18376. doi: 10.3934/math.20221011

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Study of Sturm-Liouville boundary value problems with $ {p} $ -Laplacian by using generalized form of fractional order derivative

1.
Laboratory of Mathematics and Applied Sciences, University of Ghardaia, Metlili 47000, Algeria
2.
Department of Mathematics, Hodeidah University, P. O. Box 3114, Al-Hudaydah, Yemen
3.
Department of Mathematics, Hajjah University, Hajjah, Yemen
4.
Department of Mathematics and Sciences, Prince Sultan University, P. O. Box. 66833, 11586, Riyadh, Saudi Arabia
5.
Department of Mathematics, University of Malakand, Chakdara Dir(L), P. O. Box. 18000, Khyber Pakhtunkhwa, Pakistan
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 07 March 2022 Revised: 25 July 2022 Accepted: 03 August 2022 Published: 16 August 2022
MSC : 26A33, 34A08

This manuscript is related to deriving some necessary and appropriate conditions for qualitative results about a class of Sturm-Liouville (S-L) boundary value problems (BVPs) with the $ p $ -Laplacian operator under a fractional $ \vartheta $ -Caputo type derivative. For the required results, we use Mönch's fixed point theorem with a measuring of non-compactness. Here, it is important to mention that the aforesaid equations belong to a highly significant class of problems that have many of the same properties and applications to solving various problems of dynamics and wave equations theory. For the demonstration of our theoretical results, we provide an example.
- FDEs,
- Sturm-Liouville BVPs,
- measure of non-compactness,
- Mönch's fixed point theorem,
- $ \mathrm{p} $ -Laplacian operator,
- Banach spaces
Citation: Abdelatif Boutiara, Mohammed S. Abdo, Mohammed A. Almalahi, Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad. Study of Sturm-Liouville boundary value problems with $ {p} $ -Laplacian by using generalized form of fractional order derivative[J]. AIMS Mathematics, 2022, 7(10): 18360-18376. doi: 10.3934/math.20221011

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Abstract

This manuscript is related to deriving some necessary and appropriate conditions for qualitative results about a class of Sturm-Liouville (S-L) boundary value problems (BVPs) with the $ p $ -Laplacian operator under a fractional $ \vartheta $ -Caputo type derivative. For the required results, we use Mönch's fixed point theorem with a measuring of non-compactness. Here, it is important to mention that the aforesaid equations belong to a highly significant class of problems that have many of the same properties and applications to solving various problems of dynamics and wave equations theory. For the demonstration of our theoretical results, we provide an example.

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