General characteristics of a fractal Sturm–Liouville problem
Fatma Ayça Çetinkaya, Alireza Khalili Golmankhaneh
Abstract
In this paper, we consider a regular fractal Sturm-Liouville boundary value problem. We prove the self-adjointness of the differential operator which is generated by the $F^\alpha$-derivative introduced in [32]. We obtained the $F^\alpha$-analogue of Liouville's theorem, and we show some properties of eigenvalues and eigenfunctions. We present examples to demonstrate the efficiency and applicability of the obtained results. The findings of this paper can be regarded as a contribution to an emerging field.
Topics & Concepts
Sturm–Liouville theoryMathematicsEigenfunctionEigenvalues and eigenvectorsFractalBoundary value problemOperator (biology)Mathematical analysisDifferential operatorInterval (graph theory)Field (mathematics)Pure mathematicsCombinatoricsGeneQuantum mechanicsRepressorBiochemistryPhysicsChemistryTranscription factorSpectral Theory in Mathematical PhysicsMathematical functions and polynomialsQuantum chaos and dynamical systems