On a mixed nonlinear boundary value problem with the right Caputo fractional derivative and multipoint closed boundary conditions

Bashir Ahmad; Manal Alnahdi; Sotiris K. Ntouyas; Ahmed Alsaedi; Bashir Ahmad; Manal Alnahdi; Sotiris K. Ntouyas; Ahmed Alsaedi

doi:10.3934/math.2023593

AIMS Mathematics

2023, Volume 8, Issue 5: 11709-11726. doi: 10.3934/math.2023593

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On a mixed nonlinear boundary value problem with the right Caputo fractional derivative and multipoint closed 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, 45110 Ioannina, Greece

Received: 14 December 2022 Revised: 08 March 2023 Accepted: 09 March 2023 Published: 17 March 2023
MSC : 34A08, 34B10, 34B15

This paper is concerned with the study of a new class of boundary value problems involving a right Caputo fractional derivative and mixed Riemann-Liouville fractional integral operators, and a nonlocal multipoint version of the closed boundary conditions. The proposed problem contains the usual and mixed Riemann-Liouville integrals type nonlinearities. We obtain the existence and uniqueness results with the aid of the fixed point theorems. Examples are presented for illustrating the abstract results. Our results are not only new in the given configuration but also specialize to some interesting situations.
- right Caputo fractional derivative,
- Riemann-Liouville fractional integrals,
- nonlocal multipoint closed boundary conditions,
- existence,
- fixed point
Citation: Bashir Ahmad, Manal Alnahdi, Sotiris K. Ntouyas, Ahmed Alsaedi. On a mixed nonlinear boundary value problem with the right Caputo fractional derivative and multipoint closed boundary conditions[J]. AIMS Mathematics, 2023, 8(5): 11709-11726. doi: 10.3934/math.2023593

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Abstract

This paper is concerned with the study of a new class of boundary value problems involving a right Caputo fractional derivative and mixed Riemann-Liouville fractional integral operators, and a nonlocal multipoint version of the closed boundary conditions. The proposed problem contains the usual and mixed Riemann-Liouville integrals type nonlinearities. We obtain the existence and uniqueness results with the aid of the fixed point theorems. Examples are presented for illustrating the abstract results. Our results are not only new in the given configuration but also specialize to some interesting situations.

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