Note on the conformable boundary value problems: Sturm’s theorems and Green’s function
DOI:
https://doi.org/10.31349/RevMexFis.67.471Keywords:
Conformable fractional derivative, Conformable fractional integral, Conformable fractional differential equations, Sturm´s Theorems, Green´s FunctionAbstract
Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.References
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