On a nonlinear coupled system of differential equations involving Hilfer fractional derivative and Riemann-Liouville mixed operators with nonlocal integro-multi-point boundary conditions

Ahmed Alsaedi; Bashir Ahmad; Afrah Assolami; Sotiris K. Ntouyas; Ahmed Alsaedi; Bashir Ahmad; Afrah Assolami; Sotiris K. Ntouyas

doi:10.3934/math.2022704

AIMS Mathematics

2022, Volume 7, Issue 7: 12718-12741. doi: 10.3934/math.2022704

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Research article

On a nonlinear coupled system of differential equations involving Hilfer fractional derivative and Riemann-Liouville mixed operators with nonlocal integro-multi-point boundary conditions

1.
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
2.
Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi Arabia
3.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received: 07 December 2021 Revised: 18 April 2022 Accepted: 20 April 2022 Published: 29 April 2022
MSC : 34A12, 34A40

We study a coupled system of multi-term Hilfer fractional differential equations of different orders involving non-integral and autonomous type Riemann-Liouville mixed integral nonlinearities supplemented with nonlocal coupled multi-point and Riemann-Liouville integral boundary conditions. The uniqueness result for the given problem is based on the contraction mapping principle, while the existence results are derived with the aid of Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}$'s fixed point theorem and Leray-Schauder nonlinear alternative. Examples illustrating the main results are presented.
- Hilfer fractional differential equations,
- Riemann-Liouville mixed integral operators,
- nonlocal boundary conditions,
- fixed point theorems
Citation: Ahmed Alsaedi, Bashir Ahmad, Afrah Assolami, Sotiris K. Ntouyas. On a nonlinear coupled system of differential equations involving Hilfer fractional derivative and Riemann-Liouville mixed operators with nonlocal integro-multi-point boundary conditions[J]. AIMS Mathematics, 2022, 7(7): 12718-12741. doi: 10.3934/math.2022704

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Abstract

We study a coupled system of multi-term Hilfer fractional differential equations of different orders involving non-integral and autonomous type Riemann-Liouville mixed integral nonlinearities supplemented with nonlocal coupled multi-point and Riemann-Liouville integral boundary conditions. The uniqueness result for the given problem is based on the contraction mapping principle, while the existence results are derived with the aid of Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}$'s fixed point theorem and Leray-Schauder nonlinear alternative. Examples illustrating the main results are presented.

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