Abstract
This paper deals with the analysis of Caputo variable order fractional differential equations. The main objective of the paper is to investigate the existence and uniqueness of solutions to the problem at hand. To achieve this, the paper employs the hypothesis of ordinary differential equations and derives a theorem of continuity for VOFDE. The results of the study show that there is global existence of solutions to the problem under consideration. Furthermore, the paper also establishes results for Caputo variable order FDE and demonstrates Ulam–Hyers stability. This indicates that small changes in initial conditions or parameters of the equation result in small changes in the solution of the equation. Overall, the research paper contributes to the understanding of Caputo variable order fractional differential equations and provides theoretical results that can be useful in various applications.
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Acknowledgements
Their authors extend Their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Larg Groups Research Project under grant number (RGP.2/44/44) and this study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444).
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Albasheir, N.A., Alsinai, A., Niazi, A.U.K. et al. A theoretical investigation of Caputo variable order fractional differential equations: existence, uniqueness, and stability analysis. Comp. Appl. Math. 42, 367 (2023). https://doi.org/10.1007/s40314-023-02520-6
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DOI: https://doi.org/10.1007/s40314-023-02520-6
Keywords
- Uniqueness–existence
- Ulam–Hyers stability
- Ulam–Hyers–Rassiass stability
- Variable order fractional differential equation
- Continuation theorem