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- W3204333618 abstract "Abstract In this paper, we are concerned with the eigenvalue gap and eigenvalue ratio of the Dirichlet conformable fractional Sturm–Liouville problems. We show that this kind of differential equation satisfies the Sturm–Liouville property by the Prüfer substitution. That is, the n th eigenfunction has $n-1$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:math> zero in $( 0,pi ) $ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>π</mml:mi> <mml:mo>)</mml:mo> </mml:math> for $nin mathbb{N}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:math> . Then, using the homotopy argument, we find the minimum of the first eigenvalue gap under the class of single-well potential functions and the first eigenvalue ratio under the class of single-barrier density functions. The result of the eigenvalue gap is different from the classical Sturm–Liouville problem." @default.
- W3204333618 created "2021-10-11" @default.
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- W3204333618 date "2021-09-30" @default.
- W3204333618 modified "2023-09-24" @default.
- W3204333618 title "The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems" @default.
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- W3204333618 doi "https://doi.org/10.1186/s13661-021-01556-z" @default.
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