On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces
2024

Solutions to Fractional Differential Equations in Banach Spaces

publication Evidence: high

Author Information

Author(s): Al-Shbeil Isra, Bouzid Houari, Abdelkader Benali, Lupas Alina Alp, Samei Mohammad Esmael, Alhefthi Reem K.

Primary Institution: The University of Jordan

Hypothesis

Can we establish the existence and uniqueness of solutions to multi-point nonlinear boundary value problems involving fractional differential equations with Caputo q-derivatives?

Conclusion

The study confirms the existence and uniqueness of solutions for multi-point boundary value problems involving nonlinear fractional differential equations.

Supporting Evidence

  • The study employs fixed point theory to establish results.
  • Multiple examples are provided to demonstrate the accuracy of the findings.
  • The research addresses a significant gap in the literature regarding fractional differential equations.

Takeaway

This research shows that we can find solutions to certain complex equations that involve fractional derivatives, which are used in many real-world applications.

Methodology

The authors used fixed point theory, including Banach's fixed point theorem and Leray-Schauder's alternative, to analyze the existence and uniqueness of solutions.

Digital Object Identifier (DOI)

10.1016/j.heliyon.2024.e40876

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