A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces
Abstract
:1. Introduction
2. Background Notions
- (i)
- .
- (ii)
- .
- (i)
- As , ;
- (ii)
- The spectral radius ;
- (iii)
- is non-singular and
- (iv)
- The matrices and are non-singular and non-negative, respectively.
- (i)
- ;
- (ii)
- The mapping Π is continuous and compact;
- (iii)
- The mapping Υ is an -contraction.
3. Qualitative Results
- (HP1)
- For , the functions and are bounded on the subject to bounds and , respectively.
- (HP2)
- and , , exist, where
- (HP3)
- where
4. Applications
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Boutiara, A.; Etemad, S.; Thabet, S.T.M.; Ntouyas, S.K.; Rezapour, S.; Tariboon, J. A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces. Symmetry 2023, 15, 1041. https://doi.org/10.3390/sym15051041
Boutiara A, Etemad S, Thabet STM, Ntouyas SK, Rezapour S, Tariboon J. A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces. Symmetry. 2023; 15(5):1041. https://doi.org/10.3390/sym15051041
Chicago/Turabian StyleBoutiara, Abdellatif, Sina Etemad, Sabri T. M. Thabet, Sotiris K. Ntouyas, Shahram Rezapour, and Jessada Tariboon. 2023. "A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces" Symmetry 15, no. 5: 1041. https://doi.org/10.3390/sym15051041
APA StyleBoutiara, A., Etemad, S., Thabet, S. T. M., Ntouyas, S. K., Rezapour, S., & Tariboon, J. (2023). A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces. Symmetry, 15(5), 1041. https://doi.org/10.3390/sym15051041