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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

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Open Access Research Article

Finite time stability for multi-ψ-caputa nonlinear fractional integro-differential systems

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pp. 1247–1254Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2307XML
Received:
01 May 2025
Published Online:
12 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2307
Pages:
1247–1254

Abstract

In this work, a solution for multi-ψ-caputa nonlinear fractional integro-differential systems have been studied by using ψ –Laplace transformation with Mittag-Leffler function and some necessary conditions of a nonlinear function involving ψ–R-K fractional integral to compute the finite time stability of the presented system, and all interesting conditions are illustrated by many examples.

Keywords

Subject Classifications

Primary 93A30Secondary 49K15

References

[1] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, North-Holland Mathematics Studies. Amsterdam, Netherlands: Elsevier Science (2006).
[2] T. F. Huang, B. Y. Li, and J. X. Xiong, “Test on the chaotic characteristic of Chinese futures market,” Systems Engineering, vol. 30, no. 1, pp. 43–53 (2012).
[3] M. P. Lazarević and A. M. Spasić, “Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach,” Math. Comput. Model., vol. 49, no. 3–4, pp. 475–481 (2009).
[4] F. S. Silva, D. M. Moreira, and M. A. Moret, “Conformable Laplace transform of fractional differential equations,” Axioms, vol. 7, no. 3, p. 55 (2018).
[5] F. Jarad and T. Abdeljawad, “A modified Laplace transform for certain generalized fractional operators,” Results in Nonlinear Analysis, vol. 1, no. 2, pp. 88–98 (2018).
[6] M. Wang, B. Jia, F. Du, and X. Liu, “Asymptotic stability of fractional difference equations with bounded time delays,” Fract. Calc. Appl. Anal., vol. 23, no. 2, pp. 571–590 (2020).
[7] F. Jarad and T. Abdeljawad, “Generalized fractional derivatives and Laplace transform,” Discrete & Continuous Dynamical Systems-Series S, vol. 13, no. 3 (2020). 
[8] I. Birs, I. Nascu, C. Ionescu, and C. Muresan, “Event-based fractional order control,” J. Adv. Res., vol. 25, pp. 191–203 (2020).
[9] A. Ghaffari, M. T. Kajani, and S. Effati, “Finite-time stability of nonlinear fractional differential equation with interval time-varying delay,” IEEE Trans. Automat. Contr., vol. 64, no. 12, pp. 5114–5120 (2019).
[10] I. Podlubny, “What Euler could further write, or the unnoticed ‘big bang’ of the fractional calculus,” Fract. Calc. Appl. Anal., vol. 16, no. 2, pp. 501–506 (2013).
[11] Z. Wang, J. Sun, J. Chen, and Y. Bai, “Finite-time stability of switched nonlinear time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 30, no. 7, pp. 2906–2919 (2020).
[12] C. Liang, W. Wei, and J. Wang, “Stability of delay differential equations via delayed matrix sine and cosine of polynomial degrees,” Adv. Differ. Equ., vol. 2017, no. 1, p. 131 (2017).
[13] H. S. Kadhem and S. Q. Hasan, “On Comparison Study between Double Sumudu and Elzaki Linear Transforms Method for Solving Fractional Partial Differential Equations,” Baghdad Science Journal, vol. 18, no. 3, p. 1 (2021).
[14] R. Das, J. Mishra, S. Mishra, and P. K. Pattnaik, “Design of mathematical model for the prediction of rainfall,” Journal of Interdisciplinary Mathematics, vol. 25, no. 3, pp. 587–613 (2022), doi: 10.1080/09720502.2021.2016853.

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