EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE FRACTIONAL DIFFERENTIAL EQUATION

Authors

  • Điệp Nguyễn https://llct.hitu.edu.vn/doi-ngu-nhan-su/

DOI:

https://doi.org/10.51453/3093-3706/2025/1369

Keywords:

Đạo hàm phân thứ, Phương trình vi phân, Điểm bất động

Abstract

In this paper, we investigate and prove the existence and uniqueness of solutions for the Ψ–Caputo fractional differential equation by applying the Banach and Schauder fixed point theorems under appropriate Lipschitz conditions.

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References

[1] Ricardo Almeida, A Caputo fractional derivative of a function with respect to another function, Commun Nonlinear Sci Numer Simulat 44 (2017), 460–481.

[2] J. Vanterler da C. Sousa and E. Capelas de Oliveira, On the Ψ–Hilfer fractional derivative, Commun Nonlinear Sci Numer Simulat 60 (2018), 72–91.

[3] J. Vanterler da C. Sousa and E. Capelas de Oliveira, A Gronwall inequality and the Cauchy–type problem by means of Ψ–Hilfer operator, Differential Equations & Applications 11 (2019), 87–106.

[4] D. B. Pachpatte, Properties of some Ψ–Hilfer fractional Fredholm–type integro–differential equations, Advances in Operator Theory 6 (2021), 1–14.

[5] Mohamed A. Khamsi và William A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, John Wiley & Sons, Inc. 2001.

[6] S.F. Lacroix, Traité du Calcul Différentiel et du Calcul Intégral. 2nd Edition, Mme, Paris,

Ve Courcier, Tome Troisiéme, (1819) 409–410.

[7] Bertram Ross (1977). Fractional Calculus. Mathematics Magazine, 50(3), 115–122.

[8] Niels H. Abel, Solution de quelques problemes a l’aide d’integrales definies,Oeuvres Completes, Christiania (Grondahl) 1 (1881), 16–18.

[9] J. Liouville, Mémoiresurle thèorémedes complèmentaires, J.Reine Angew. Math., 11 (1834) 1–19.

[10] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006.

Published

2025-12-28

How to Cite

Nguyễn, Điệp. (2025). EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE FRACTIONAL DIFFERENTIAL EQUATION. SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY, 11(2). https://doi.org/10.51453/3093-3706/2025/1369

Issue

Section

Natural Science and Technology

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