TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

A study of coupled fractional differential system with nonlocal integral conditions : Existence and uniqueness, Ulam-Hyers stabilty

* , ,

* Corresponding author · click or hover a name for details

pp. 473–484Vol. 28Issue 2March 2025DOI: 10.47974/JIM-1784XML
Received:
16 Nov 2022
Published Online:
15 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-1784
Pages:
473–484

Abstract

This paper deals with a new class of nonlinear coupled fractional differential equations with Caputo derivative. The existence and uniqueness of the solution is treated using the Banach mapping principle, also some results of the stability in the sens of Ulam-Hyers are introduced.

Keywords

Subject Classifications

26A3334A0834B1074G30

References

[1] A. Alsaid, N. Alghamdi, R. P. Agarwal, S. K. Ntouyas, and B. Ahmed, “Multi-term fractional-order boundary-value problems with nonlocal integral boundary conditions,” Electron. J. Diff. Eq., vol. 2018, no. 87 (2018).
[2] B. Ahmad, N. Alghamdi, A. Alsaedi, and S. K. Ntouyas, “Existence theory for a system of coupled multi-term fractional differential equations with integral multi-strip coupled boundary conditions,” Math. Meth. Appl. Sci., pp. 1-18 (2019). [Online]. Available: https://doi.org/10.1002/mma.5788.
[3] T. M. Atanackovic, M. Janev, and S. Pilipovic, “On the thermodynamical restrictions in isothermal deformations of fractional Burgers model,” Phil. Trans. R. Soc. A, vol. 378, no. 20190278 (2019). [Online]. Available: http://dx.doi.org/10.1098/rsta.2019.0278.
[4] Z. Bekkouche and Z. Dahmani, “New problem of sequential differential equations with nonlocal conditions,” J. Interdiscip. Math., pp. 1-20 (2021). [Online]. Available: https://doi.org/10.1080/09720502.2020.1833446.
[5] R. Ozarslan and Y. Sekerci, “Fractional order oxygen–plankton system under climate change,” Chaos, vol. 30, no. 033131 (2020). [Online]. Available: https://doi.org/10.1063/1.5129766.
[6] R. A. Magomedov, R. R. Meilanov, R. P. Meilanov, E. N. Akhmedov, V. D. Beybalaev, and A. A. Aliverdiev, “Generalization of thermodynamics in fractional-order derivatives and calculation of heat-transfer properties of noble gases,” J. Therm. Anal. Calorim., vol. 1189, pp. 1194 (2018). [Online]. Available: https://doi.org/10.1007/s10973-018-7024-2.
[7] R. Matusu, “Application of fractional order calculus to control theory,” Int. J. Math. Models Methods Appl. Sci., vol. 5, no. 7, pp. 1162-1169 (2011).
[8] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Yverdon, Switzerland: Gordon and Breach Science (1993).
[9] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering. San Diego, CA, USA: Academic Press (1999).
[10] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam, The Netherlands: Elsevier Science (2006).
[11] V. E. Tarasov, “On history of mathematical economics: applications of fractional calculus,” Mathematics, vol. 7, no. 6, p. 509 (2019). [Online]. Available: https://doi.org/10.3390/math7060509.
[12] J. A. Tenreito Machado, I. S. Jesus, R. Barbosa, and M. F. Silva, “Application of fractional calculus in engineering.”
[13] J. A. Tenreito Machado, M. E. Mata, and A. M. Lopes, “Fractional dynamics and pseudo-phase space of country economic processes,” Mathematics, vol. 8, no. 81 (2020). [Online]. Available: https://doi.org/10.3390/math8010081.
[14] R. P. Meilanov and R. Magomedov, “Thermodynamics in fractional calculus,” J. Eng. Phys. Thermophys., vol. 87, no. 6, pp. 1521-1531 (2014). [Online]. Available: https://doi.org/10.1007/s10891-014-1158-2.

Views: 173Downloads: 78Citations: 0