Separated boundary value problems via quantum Hilfer and Caputo operators

Idris Ahmed; Sotiris K. Ntouyas; Jessada Tariboon; Idris Ahmed; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.2024949

AIMS Mathematics

2024, Volume 9, Issue 7: 19473-19494. doi: 10.3934/math.2024949

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Research article

Separated boundary value problems via quantum Hilfer and Caputo operators

1.
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
2.
Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University, P.M.B 048 Kafin-Hausa, Jigawa State, Nigeria
3.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received: 01 May 2024 Revised: 27 May 2024 Accepted: 07 June 2024 Published: 13 June 2024
MSC : 26A33, 34A12, 34A34, 34D20

This paper describes a new class of boundary value fractional-order differential equations of the $ q $-Hilfer and $ q $-Caputo types, with separated boundary conditions. The presented problem is converted to an equivalent integral form, and fixed-point theorems are used to prove the existence and uniqueness of solutions. Moreover, several special cases demonstrate how the proposed problems advance beyond the existing literature. Examples are provided to support the analysis presented.
- Hilfer fractional derivative,
- Caputo derivative,
- separated boundary condition,
- existence,
- fixed point theorems
Citation: Idris Ahmed, Sotiris K. Ntouyas, Jessada Tariboon. Separated boundary value problems via quantum Hilfer and Caputo operators[J]. AIMS Mathematics, 2024, 9(7): 19473-19494. doi: 10.3934/math.2024949

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Abstract

This paper describes a new class of boundary value fractional-order differential equations of the $ q $-Hilfer and $ q $-Caputo types, with separated boundary conditions. The presented problem is converted to an equivalent integral form, and fixed-point theorems are used to prove the existence and uniqueness of solutions. Moreover, several special cases demonstrate how the proposed problems advance beyond the existing literature. Examples are provided to support the analysis presented.

References

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