Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order

M. Manigandan; Subramanian Muthaiah; T. Nandhagopal; R. Vadivel; B. Unyong; N. Gunasekaran; M. Manigandan; Subramanian Muthaiah; T. Nandhagopal; R. Vadivel; B. Unyong; N. Gunasekaran

doi:10.3934/math.2022045

AIMS Mathematics

2022, Volume 7, Issue 1: 723-755. doi: 10.3934/math.2022045

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Research article

Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order

1.
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India
2.
Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, India
3.
Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand
4.
Computational Intelligence Laboratory, Toyota Technological Institute, Nagoya, 468-8511, Japan

Received: 26 August 2021 Accepted: 12 October 2021 Published: 15 October 2021
MSC : 26A33, 34A08, 34B15

In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.
- Caputo derivatives,
- coupled system,
- fixed point,
- fractional differential equations(FDEs),
- inclusions,
- sequential derivatives
Citation: M. Manigandan, Subramanian Muthaiah, T. Nandhagopal, R. Vadivel, B. Unyong, N. Gunasekaran. Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order[J]. AIMS Mathematics, 2022, 7(1): 723-755. doi: 10.3934/math.2022045

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Abstract

In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.

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