Conformable fractional Sturm‐Liouville equation
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DOI: 10.1002/mma.5595
Abstract: In this article, we discuss a conformable fractional Sturm‐Liouville boundary‐value problem. We prove an existence and uniqueness theorem for this equation and formulate a self‐adjoint boundary value problem. We also construct the associated Green function… read more here.
Keywords: liouville equation; fractional sturm; sturm liouville; conformable fractional ... See more keywords
β−type fractional Sturm‐Liouville Coulomb operator and applied results
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DOI: 10.1002/mma.5769
Abstract: 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… read more here.
Keywords: fractional sturm; sturm liouville; liouville coulomb; operator ... See more keywords
The transmutation operator method for efficient solution of the inverse Sturm‐Liouville problem on a half‐line
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DOI: 10.1002/mma.5854
Abstract: The inverse Sturm‐Liouville problem on a half‐line is considered. With the aid of a Fourier‐Legendre series representation of the transmutation integral kernel and the Gel'fand‐Levitan equation, the numerical solution of the problem is reduced to… read more here.
Keywords: half line; inverse sturm; problem; problem half ... See more keywords
On the resolvent of singular Sturm‐Liouville operators with transmission conditions
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DOI: 10.1002/mma.6193
Abstract: In this article, we investigate the resolvent operator of singular Sturm‐Liouville problem with transmission conditions. We obtain integral representations for the resolvent of this operator in terms of the spectral function. Later, we discuss some… read more here.
Keywords: sturm liouville; singular sturm; transmission conditions; resolvent operator ... See more keywords
Solvability of an inverse problem for discontinuous Sturm–Liouville operators
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DOI: 10.1002/mma.6713
Abstract: In this paper, we consider the Sturm–Liouville equation with the jump conditions inside the interval (0,π). The inverse problem is studied, which consists in recovering operator coefficients from two spectra, corresponding to different boundary conditions.… read more here.
Keywords: problem; inverse problem; sturm liouville; problem discontinuous ... See more keywords
Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition
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DOI: 10.1002/mma.7375
Abstract: there exists a unique function q̃ ∈ L2(0, π) such that ω = ?̃? and {K̃,Ñ} are the Cauchy data of q̃.” The reason of condition (*) is that the Cauchy data are related with… read more here.
Keywords: stability inverse; inverse sturm; solvability stability; condition ... See more keywords
Solving Symmetric Inverse Sturm–Liouville Problem Using Chebyshev Polynomials
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DOI: 10.1007/s00009-019-1330-1
Abstract: In this study, we consider Sturm–Liouville equation having a symmetric potential function under the separated boundary conditions on a finite interval. Then, we use Chebyshev polynomials of the first kind for calculating the approximate solution… read more here.
Keywords: liouville; liouville problem; sturm liouville; inverse sturm ... See more keywords
Spectral Analysis of Singular Matrix-Valued Sturm–Liouville Operators
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DOI: 10.1007/s00009-019-1357-3
Abstract: In the Hilbert space $$L_{W}^{2}([a,b);E)$$LW2([a,b);E) ($$-\infty0$$W>0) a space of boundary values of the symmetric singular matrix-valued Sturm–Liouville operator with maximal deficiency indices (2N, 2N) (in limit-circle case at singular end point b) is constructed. With the… read more here.
Keywords: sturm liouville; valued sturm; matrix; operator ... See more keywords
Traces for Sturm–Liouville Operators with Frozen Argument on Star Graphs
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DOI: 10.1007/s00025-020-1165-x
Abstract: In this paper, Sturm-Liouville operators with frozen argument on star graphs are studied. First, we derive the asymptotic expression for the large eigenvalues. Second, the regularized trace formulae for these operators are calculated with the… read more here.
Keywords: sturm liouville; frozen argument; operators frozen; star graphs ... See more keywords
Fractional Sturm–Liouville Equations: Self-Adjoint Extensions
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DOI: 10.1007/s11785-018-0828-z
Abstract: In this report we study a fractional analogue of Sturm–Liouville equation. A class of self-adjoint fractional Sturm–Liouville operators is described. We give a biological interpretation of the fractional order equation and nonlocal boundary conditions that… read more here.
Keywords: sturm liouville; liouville equations; sturm; fractional sturm ... See more keywords
Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions
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DOI: 10.1007/s12591-020-00520-0
Abstract: In this study, we consider the singular Sturm-Liouville (S-L) problem with transmission conditions (TC). The eigenvalues of the singular S-L problem with TC are investigated. By defining a new Hilbert space which is related to… read more here.
Keywords: sturm liouville; liouville problem; eigenvalues singular; problem transmission ... See more keywords