Solvability and Stability of a Coupled System of Multi-Term Fractional Differential Equations

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DOI: https://doi.org/10.28924/2291-8639-24-2026-291
Published: Sep 21, 2026
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Maryam Ahmad Alyami, Najla Alghamdi, Kifah Alotaibi, Saleh S. Redhwan, Solvability and Stability of a Coupled System of Multi-Term Fractional Differential Equations, Int. J. Anal. Appl., 24 (2026), 291.

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Maryam Ahmad Alyami, Najla Alghamdi, Kifah Alotaibi, Saleh S. Redhwan

Abstract

In this work, we carry out a detailed qualitative analysis of a coupled system of multi-term fractional differential equations. More specifically, we investigate whether solutions exist and whether they are unique. The system under study includes coupled nonlocal boundary conditions. To obtain our results, we employ appropriate fixed-point methods that are well-suited to fractional problems. Beyond existence and uniqueness, we also conduct a thorough evaluation of the model's stability properties. Specifically, we examine Ulam-Hyers-type stability and its generalized version. These stability analyses confirm that the proposed system is reliable under small perturbations.

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References

  1. B. Ahmad, N. Alghamdi, A. Alsaedi, S.K. Ntouyas, A System of Coupled Multi-Term Fractional Differential Equations with Three-Point Coupled Boundary Conditions, Fract. Calc. Appl. Anal. 22 (2019), 601–616. https://doi.org/10.1515/fca-2019-0034.
  2. B. Ahmad, N. Alghamdi, A. Alsaedi, S.K. Ntouyas, Existence Theory for a System of Coupled Multi-Term Fractional Differential Equations with Integral Multi-Strip Coupled Boundary Conditions, Math. Methods Appl. Sci. 44 (2021), 2325–2342. https://doi.org/10.1002/mma.5788.
  3. B. Ahmad, A. Alsaedi, N. Alghamdi, S.K. Ntouyas, Existence Theorems for a Coupled System of Nonlinear Multi-Term Fractional Differential Equations with Nonlocal Boundary Conditions, Kragujevac J. Math. 46 (2022), 317–331. https://doi.org/10.46793/KgJMat2202.317A.
  4. G. Mani, P. Ganesh, P. Ramasamy, S. Aljohani, N. Mlaiki, Existence and Stability Results for a Coupled Multi-Term Caputo Fractional Differential Equations, Fixed Point Theory Algorithms Sci. Eng. 2025 (2025), 6. https://doi.org/10.1186/s13663-025-00789-2.
  5. P. Wang, B. Han, J. Bao, The Existence and Ulam Stability Analysis of a Multi-Term Implicit Fractional Differential Equation with Boundary Conditions, Fractal Fract. 8 (2024), 311. https://doi.org/10.3390/fractalfract8060311.
  6. R. Almeida, A Unified Approach to Implicit Fractional Differential Equations with Anti-Periodic Boundary Conditions, Mathematics 13 (2025), 2890. https://doi.org/10.3390/math13172890.
  7. M. Asif, A. Zada, A. Avram, Qualitative Analysis of a Coupled System with Nonlinear Mixed Fractional Integro-Differential Equation Involving Caputo Fractional Derivative, J. Math. Comput. Sci. 38 (2024), 56–79. https://doi.org/10.22436/jmcs.038.01.05.
  8. S. Picozzi, B.J. West, Fractional Langevin Model of Memory in Financial Markets, Phys. Rev. E 66 (2002), 046118. https://doi.org/10.1103/PhysRevE.66.046118.
  9. R. Hilfer, Threefold Introduction to Fractional Derivatives, in: Anomalous Transport: Foundations and Applications, Wiley-VCH, Weinheim, 2008, pp. 17–73. https://doi.org/10.1002/9783527622979.ch2.
  10. R. Schumer, D.A. Benson, M.M. Meerschaert, S.W. Wheatcraft, Eulerian Derivation of the Fractional Advection–Dispersion Equation, J. Contam. Hydrol. 48 (2001), 69–88. https://doi.org/10.1016/S0169-7722(00)00170-4.
  11. A.A.M. Arafa, S.Z. Rida, M. Khalil, Fractional Modeling Dynamics of HIV and CD4+ T-Cells during Primary Infection, Nonlinear Biomed. Phys. 6 (2012), 1. https://doi.org/10.1186/1753-4631-6-1.
  12. A. Carvalho, C.M.A. Pinto, A Delay Fractional Order Model for the Co-infection of Malaria and HIV/AIDS, Int. J. Dyn. Control 5 (2017), 168–186. https://doi.org/10.1007/s40435-016-0224-3.
  13. R.P. Chauhan, S. Kumar, B.S.T. Alkahtani, S.S. Alzaid, A Study on Fractional Order Financial Model by Using Caputo–Fabrizio Derivative, Results Phys. 57 (2024), 107335. https://doi.org/10.1016/j.rinp.2024.107335.
  14. T. Jin, X. Yang, Monotonicity Theorem for the Uncertain Fractional Differential Equation and Application to Uncertain Financial Market, Math. Comput. Simul. 190 (2021), 203–221. https://doi.org/10.1016/j.matcom.2021.05.018.
  15. M. Javidi, B. Ahmad, Dynamic Analysis of Time Fractional Order Phytoplankton–Toxic Phytoplankton–Zooplankton System, Ecol. Model. 318 (2015), 8–18. https://doi.org/10.1016/j.ecolmodel.2015.06.016.
  16. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier, Amsterdam, 2006. https://doi.org/10.1016/S0304-0208(06)X8001-5.
  17. B. Ahmad, S.K. Ntouyas, J. Tariboon, Quantum Calculus: New Concepts, Impulsive IVPs and BVPs, Inequalities, Trends in Abstract and Applied Analysis 4, World Scientific, Singapore, 2016. https://doi.org/10.1142/10075.
  18. A. Granas, J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, 2003. https://doi.org/10.1007/978-0-387-21593-8.