Nonlinear multi-term fractional differential equations with Riemann-Stieltjes integro-multipoint boundary conditions

Bashir Ahmad; Ahmed Alsaedi; Ymnah Alruwaily; Sotiris K. Ntouyas; Bashir Ahmad; Ahmed Alsaedi; Ymnah Alruwaily; Sotiris K. Ntouyas

doi:10.3934/math.2020099

AIMS Mathematics

2020, Volume 5, Issue 2: 1446-1461. doi: 10.3934/math.2020099

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Research article

Nonlinear multi-term fractional differential equations with Riemann-Stieltjes integro-multipoint 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 Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received: 11 November 2019 Accepted: 09 January 2020 Published: 21 January 2020
MSC : 34A08, 34B10, 34B15

In this paper, we consider a nonlinear multi-term Caputo fractional differential equation with nonlinearity depending on the unknown function together with its lower-order Caputo fractional derivatives and equipped with Riemann-Stieltjes integro multipoint boundary conditions. The given problem is transformed to an equivalent fixed point problem, which is then solved with the aid of standard fixed point theorems to establish the existence and uniqueness results for the problem at hand. Examples are constructed for the illustration of the obtained results.
- Caputo derivative,
- Riemann-Stieltjes integral,
- multipoint boundary conditions,
- existence of solutions,
- fixed point
Citation: Bashir Ahmad, Ahmed Alsaedi, Ymnah Alruwaily, Sotiris K. Ntouyas. Nonlinear multi-term fractional differential equations with Riemann-Stieltjes integro-multipoint boundary conditions[J]. AIMS Mathematics, 2020, 5(2): 1446-1461. doi: 10.3934/math.2020099

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Abstract

In this paper, we consider a nonlinear multi-term Caputo fractional differential equation with nonlinearity depending on the unknown function together with its lower-order Caputo fractional derivatives and equipped with Riemann-Stieltjes integro multipoint boundary conditions. The given problem is transformed to an equivalent fixed point problem, which is then solved with the aid of standard fixed point theorems to establish the existence and uniqueness results for the problem at hand. Examples are constructed for the illustration of the obtained results.

References

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