Nonlocal coupled hybrid fractional system of mixed fractional derivatives via an extension of Darbo's theorem

Ayub Samadi; Sotiris K. Ntouyas; Jessada Tariboon; Ayub Samadi; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.2021232

AIMS Mathematics

2021, Volume 6, Issue 4: 3915-3926. doi: 10.3934/math.2021232

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Nonlocal coupled hybrid fractional system of mixed fractional derivatives via an extension of Darbo's theorem

1.
Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran
2.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece
4.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 16 December 2020 Accepted: 29 January 2021 Published: 02 February 2021
MSC : 47H08, 47H10, 26A33, 34A08

In this work a new existence result is established for a coupled fractional system consisting of one Caputo and one Riemann-Liouville fractional derivatives and nonlocal hybrid boundary conditions. A new generalization of Darbo's theorem associated with measures of noncompactness is the main tool in our approach. An example is constructed to justify the theoretical result.
- fractional derivative,
- Hybrid differential equation,
- measure of noncompactness,
- coupled system,
- fixed point
Citation: Ayub Samadi, Sotiris K. Ntouyas, Jessada Tariboon. Nonlocal coupled hybrid fractional system of mixed fractional derivatives via an extension of Darbo's theorem[J]. AIMS Mathematics, 2021, 6(4): 3915-3926. doi: 10.3934/math.2021232

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Abstract

In this work a new existence result is established for a coupled fractional system consisting of one Caputo and one Riemann-Liouville fractional derivatives and nonlocal hybrid boundary conditions. A new generalization of Darbo's theorem associated with measures of noncompactness is the main tool in our approach. An example is constructed to justify the theoretical result.

References

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