Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann–Liouville Boundary Conditions
Abstract
1. Introduction
- Fundamental concepts and auxiliary lemmas related to the linear variant of problem (2), providing a solid theoretical foundation for our subsequent analysis.
- The concerning problem (2), derived using standard fixed-point theorems. This section demonstrates the rigorous application of these mathematical tools to establish the existence and uniqueness of solutions.
- We investigate the stability properties of the system of nonlinear coupled SFDEs of the Caputo type through UH stability analysis. This section highlights the robustness of the solutions and their resilience to small perturbations, which is essential for practical implementations.
- Finally, we provide detailed proofs and examples to further illustrate our findings. The numerical section ensures that the theoretical results are well-supported by concrete instances, enhancing the understanding and applicability of our work.
2. Preliminaries
3. Main Results
- ∃ continuous non-negative functions and for , such that
- ∃ positive constants , , and such that ∀,
4. Stability Results
5. Examples
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
c.c | completely continuous |
BVP | Boundary Value Problems |
UH | Ulam–Hyers |
FDEs | Fractional Differential Equations |
SFD | Sequential Fractional Differential |
CFDs | Caputo Fractional Derivatives |
SFDEs | Sequential Fractional Differential Equations |
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Gunasekaran, N.; Manigandan, M.; Vinoth, S.; Vadivel, R. Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann–Liouville Boundary Conditions. Fractal Fract. 2024, 8, 457. https://doi.org/10.3390/fractalfract8080457
Gunasekaran N, Manigandan M, Vinoth S, Vadivel R. Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann–Liouville Boundary Conditions. Fractal and Fractional. 2024; 8(8):457. https://doi.org/10.3390/fractalfract8080457
Chicago/Turabian StyleGunasekaran, Nallappan, Murugesan Manigandan, Seralan Vinoth, and Rajarathinam Vadivel. 2024. "Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann–Liouville Boundary Conditions" Fractal and Fractional 8, no. 8: 457. https://doi.org/10.3390/fractalfract8080457
APA StyleGunasekaran, N., Manigandan, M., Vinoth, S., & Vadivel, R. (2024). Analysis of Caputo Sequential Fractional Differential Equations with Generalized Riemann–Liouville Boundary Conditions. Fractal and Fractional, 8(8), 457. https://doi.org/10.3390/fractalfract8080457