Reconstruction of Singular Second-order Differential Equations From Spectral Characteristics

Mosazadeh, Seyfollah

doi:10.1007/s10255-019-0838-2

Acta Math. Appl. Sin. Engl. Ser.

2019

DOI: 10.1007/s10255-019-0838-2

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Reconstruction of Singular Second-order Differential Equations From Spectral Characteristics

Seyfollah Mosazadeh

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2024

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Spectral and Oscillation Theory for an Unconventional Fractional Sturm–Liouville Problem

Dehghan,

Mingarelli

2024

Fractal Fract

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Here, we investigate the spectral and oscillation theory for a class of fractional differential equations subject to specific boundary conditions. By transforming the problem into a modified version with a classical structure, we establish the orthogonality properties of eigenfunctions and some major comparison theorems for solutions. We also derive a new type of integration by using parts of formulas for modified fractional integrals and derivatives. Furthermore, we analyze the variational characterization of the first eigenvalue, revealing its non-zero first eigenfunction within the interior. Our findings demonstrate the potential for novel definitions of fractional derivatives to mirror the classical Sturm–Liouville theory through simple isospectral transformations.

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Spectral and Oscillation Theory for an Unconventional Fractional Sturm–Liouville Problem

Dehghan,

Mingarelli

2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

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Reconstruction of Singular Second-order Differential Equations From Spectral Characteristics

Cited by 1 publication

References 11 publications

Spectral and Oscillation Theory for an Unconventional Fractional Sturm–Liouville Problem

Spectral and Oscillation Theory for an Unconventional Fractional Sturm–Liouville Problem

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