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β −type fractional Sturm‐Liouville Coulomb operator and applied results
Author(s) -
Ozarslan Ramazan,
Ercan Ahu,
Bas Erdal
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5769
Subject(s) - mathematics , sturm–liouville theory , eigenfunction , fractional calculus , operator (biology) , eigenvalues and eigenvectors , type (biology) , spectral theory of ordinary differential equations , context (archaeology) , mathematical analysis , spectral properties , pure mathematics , finite rank operator , quasinormal operator , boundary value problem , quantum mechanics , physics , ecology , biochemistry , chemistry , paleontology , repressor , biology , astrophysics , transcription factor , banach space , gene
In this article, β ‐type fractional Sturm‐Liouville Coulomb operator is considered by Hilfer fractional derivative. Fundamental spectral theory is investigated for the aforementioned problem. In this context, it is shown that the operator is self‐adjoint, eigenfunctions correspond to the distinct eigenfunctions are orthogonal, and eigenvalues are real. Furthermore, applications of this problem are given by the Adomian decomposition method and the results are shown with visual graphs.