On a general class of $ n $th order sequential hybrid fractional differential equations with boundary conditions

Shaista Gul; Rahmat Ali Khan; Kamal Shah; Thabet Abdeljawad; Shaista Gul; Rahmat Ali Khan; Kamal Shah; Thabet Abdeljawad

doi:10.3934/math.2023491

AIMS Mathematics

2023, Volume 8, Issue 4: 9740-9760. doi: 10.3934/math.2023491

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On a general class of $ n $th order sequential hybrid fractional differential equations with boundary conditions

1.
Department of Mathematics, University of Malakand, Chakdara, Dir(L), 18000, KPK, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
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: 07 December 2022 Revised: 28 January 2023 Accepted: 28 January 2023 Published: 21 February 2023
MSC : 34A08, 34A12, 47H10

This manuscript is related to consider a general class of $ n $th order sequential hybrid fractional differential equations (S-HFDEs) with boundary conditions. With the help of the coincidence degree theory of topology, some appropriate results for the existence theory of the aforementioned class are developed. The mentioned degree theory is a powerful tool to investigate nonlinear problems for qualitative theory. A result related to Ulam-Hyers (U-H) stability is also developed for the considered problem. It should be kept in mind that the considered degree theory relaxes the strong compact condition by some weaker one. Hence, it is used as a sophisticated tool in the investigation of the existence theory of solutions to nonlinear problems. Also, an example is given.
- fractional Caputo derivative,
- sequential hybrid fractional differential equations,
- degree theory,
- Ulam-Hyers stability
Citation: Shaista Gul, Rahmat Ali Khan, Kamal Shah, Thabet Abdeljawad. On a general class of $ n $th order sequential hybrid fractional differential equations with boundary conditions[J]. AIMS Mathematics, 2023, 8(4): 9740-9760. doi: 10.3934/math.2023491

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Abstract

This manuscript is related to consider a general class of $ n $th order sequential hybrid fractional differential equations (S-HFDEs) with boundary conditions. With the help of the coincidence degree theory of topology, some appropriate results for the existence theory of the aforementioned class are developed. The mentioned degree theory is a powerful tool to investigate nonlinear problems for qualitative theory. A result related to Ulam-Hyers (U-H) stability is also developed for the considered problem. It should be kept in mind that the considered degree theory relaxes the strong compact condition by some weaker one. Hence, it is used as a sophisticated tool in the investigation of the existence theory of solutions to nonlinear problems. Also, an example is given.

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