Lyapunov Inequalities for Two Dimensional Fractional Boundary-Value Problems with Mixed Fractional Derivatives
Abstract
:1. Introduction
- We obtain the Lyapunov-type inequalities, which provide the necessary conditions for the existence of nonzero positive solutions. Thanks to this, we can indicate when the nontrivial positive solution to the problem does not exist.
- Mixed fractional derivatives are considered, and because of that we can establish a connection to the fractional calculus of variations.
2. Preliminaries
3. Partial Differential Equation of the First Type
4. Partial Differential Equation of the Second Type
5. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Odzijewicz, T. Lyapunov Inequalities for Two Dimensional Fractional Boundary-Value Problems with Mixed Fractional Derivatives. Axioms 2023, 12, 301. https://doi.org/10.3390/axioms12030301
Odzijewicz T. Lyapunov Inequalities for Two Dimensional Fractional Boundary-Value Problems with Mixed Fractional Derivatives. Axioms. 2023; 12(3):301. https://doi.org/10.3390/axioms12030301
Chicago/Turabian StyleOdzijewicz, Tatiana. 2023. "Lyapunov Inequalities for Two Dimensional Fractional Boundary-Value Problems with Mixed Fractional Derivatives" Axioms 12, no. 3: 301. https://doi.org/10.3390/axioms12030301