On a coupled system under coupled integral boundary conditions involving non-singular differential operator

Kamal Shah; Thabet Abdeljawad; Bahaaeldin Abdalla; Kamal Shah; Thabet Abdeljawad; Bahaaeldin Abdalla

doi:10.3934/math.2023500

AIMS Mathematics

2023, Volume 8, Issue 4: 9890-9910. doi: 10.3934/math.2023500

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On a coupled system under coupled integral boundary conditions involving non-singular differential operator

1.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Mathematics, University of Malakand, Chakdara, Dir(L), 18000, KPK, Pakistan
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea

Received: 30 October 2022 Revised: 12 February 2023 Accepted: 16 February 2023 Published: 23 February 2023
MSC : 34A08, 34A12, 47H10

In this work, a coupled system under coupled integral boundary conditions with Caputo-Fabrizio derivative (CFD) is considered. We intend to derive some necessary and sufficient results for the existence of at least one solution. In addition, we extend our analysis further to develop a monotone iterative scheme coupled with the upper and lower solution method to compute extremal solutions. Therefore, in this regard, Perov's fixed point theorem is applied to study the existing criteria for the solution. Also, results related to at least one solution are derived by using Schauder's fixed point theorem. Finally, we use a monotone iterative procedure together with upper and lower solution methods to study extremal solutions. Graphical presentations of upper and lower solutions are provided for some examples to illustrate our results.
- Caputo-Fabrizio derivative,
- coupled integral boundary conditions,
- Perov's theorem,
- iterative procedure
Citation: Kamal Shah, Thabet Abdeljawad, Bahaaeldin Abdalla. On a coupled system under coupled integral boundary conditions involving non-singular differential operator[J]. AIMS Mathematics, 2023, 8(4): 9890-9910. doi: 10.3934/math.2023500

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Abstract

In this work, a coupled system under coupled integral boundary conditions with Caputo-Fabrizio derivative (CFD) is considered. We intend to derive some necessary and sufficient results for the existence of at least one solution. In addition, we extend our analysis further to develop a monotone iterative scheme coupled with the upper and lower solution method to compute extremal solutions. Therefore, in this regard, Perov's fixed point theorem is applied to study the existing criteria for the solution. Also, results related to at least one solution are derived by using Schauder's fixed point theorem. Finally, we use a monotone iterative procedure together with upper and lower solution methods to study extremal solutions. Graphical presentations of upper and lower solutions are provided for some examples to illustrate our results.

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