Existence of solutions by fixed point theorem of general delay fractional differential equation with $ p $-Laplacian operator

Kirti Kaushik; Anoop Kumar; Aziz Khan; Thabet Abdeljawad; Kirti Kaushik; Anoop Kumar; Aziz Khan; Thabet Abdeljawad

doi:10.3934/math.2023514

AIMS Mathematics

2023, Volume 8, Issue 5: 10160-10176. doi: 10.3934/math.2023514

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Existence of solutions by fixed point theorem of general delay fractional differential equation with $ p $-Laplacian operator

1.
Department of Mathematics and Statistics, Central University of Punjab, Bathinda 151401, India
2.
Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics, Kyung Hee University, Kyungheedae-ro 26, Dongdaemun-gu, Seoul 02447, Korea

Received: 07 October 2022 Revised: 02 February 2023 Accepted: 06 February 2023 Published: 24 February 2023
MSC : 45ND5, 34BB2, 26A33

In this manuscript, the main objective is to analyze the existence, uniqueness, (EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary conditions utilizing $ \phi_p $-Laplacian operator. To continue, we will apply Green's function to determine the suggested FDE's equivalent integral form. The Guo-Krasnosel'skii fixed point theorem and the properties of the $ p $-Laplacian operator are utilized to derive the existence results. Hyers-Ulam (HU) stability is additionally evaluated. Further, an application is presented to validate the effectiveness of the result.
- Riemann-Liouville integral,
- Caputo's derivative,
- Green's function,
- fixed point theorems,
- Hyres-Ulam stability
Citation: Kirti Kaushik, Anoop Kumar, Aziz Khan, Thabet Abdeljawad. Existence of solutions by fixed point theorem of general delay fractional differential equation with $ p $-Laplacian operator[J]. AIMS Mathematics, 2023, 8(5): 10160-10176. doi: 10.3934/math.2023514

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Abstract

In this manuscript, the main objective is to analyze the existence, uniqueness, (EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary conditions utilizing $ \phi_p $-Laplacian operator. To continue, we will apply Green's function to determine the suggested FDE's equivalent integral form. The Guo-Krasnosel'skii fixed point theorem and the properties of the $ p $-Laplacian operator are utilized to derive the existence results. Hyers-Ulam (HU) stability is additionally evaluated. Further, an application is presented to validate the effectiveness of the result.

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