Inverse problems for a conformable fractional Sturm–Liouville operator

İbrahi̇m Adalar, A. Sinan Ozkan

2020Journal of Inverse and Ill-Posed Problems25 citationsDOI

Abstract

Abstract In this paper, a Sturm–Liouville boundary value problem which includes conformable fractional derivatives of order α, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>0</m:mn> <m:mo><</m:mo> <m:mi>α</m:mi> <m:mo>≤</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {0<\alpha\leq 1} is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra and classical spectral data. We also study the half-inverse problem and prove a Hochstadt–Lieberman-type theorem.

Topics & Concepts

Conformable matrixSturm–Liouville theoryMathematicsUniquenessInverse problemInverseBoundary value problemUniqueness theorem for Poisson's equationOperator (biology)Type (biology)Pure mathematicsMathematical analysisApplied mathematicsPhysicsChemistryGeometryRepressorBiologyQuantum mechanicsGeneBiochemistryTranscription factorEcologyNumerical methods in inverse problemsFractional Differential Equations SolutionsSpectral Theory in Mathematical Physics