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Volume 6, Issue 3
Discontinuous Fractional Sturm-Liouville Problems with Hilfer Derivatives

Le Zhou, Xiaoling Hao & Kun Li

DOI: 10.12150/jnma.2024.775

J. Nonl. Mod. Anal., 6 (2024), pp. 775-792.

Published online: 2024-08

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  • Abstract

In this paper, we study discontinuous Sturm-Liouville problem with fractional Hilfer derivatives. By defining an operator $A$ in the Hilbert space $L_2[−1, 1],$ this research shows that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the constructed operator. Moreover, the characteristic function is also constructed such that the eigenvalues of the problem are coincide with the zeros of this function.

  • Keywords

Sturm-Liouville problem, Hilfer derivatives, eigenparameter, fractional boundary conditions, fractional transmission conditions.

  • AMS Subject Headings

34L05, 34B24

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-6-775, author = {Zhou , LeHao , Xiaoling and Li , Kun}, title = {Discontinuous Fractional Sturm-Liouville Problems with Hilfer Derivatives}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {3}, pages = {775--792}, abstract = {

In this paper, we study discontinuous Sturm-Liouville problem with fractional Hilfer derivatives. By defining an operator $A$ in the Hilbert space $L_2[−1, 1],$ this research shows that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the constructed operator. Moreover, the characteristic function is also constructed such that the eigenvalues of the problem are coincide with the zeros of this function.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.775}, url = {http://global-sci.org/intro/article_detail/jnma/23362.html} }
TY - JOUR T1 - Discontinuous Fractional Sturm-Liouville Problems with Hilfer Derivatives AU - Zhou , Le AU - Hao , Xiaoling AU - Li , Kun JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 775 EP - 792 PY - 2024 DA - 2024/08 SN - 6 DO - http://doi.org/10.12150/jnma.2024.775 UR - https://global-sci.org/intro/article_detail/jnma/23362.html KW - Sturm-Liouville problem, Hilfer derivatives, eigenparameter, fractional boundary conditions, fractional transmission conditions. AB -

In this paper, we study discontinuous Sturm-Liouville problem with fractional Hilfer derivatives. By defining an operator $A$ in the Hilbert space $L_2[−1, 1],$ this research shows that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the constructed operator. Moreover, the characteristic function is also constructed such that the eigenvalues of the problem are coincide with the zeros of this function.

Le Zhou, Xiaoling Hao & Kun Li. (2024). Discontinuous Fractional Sturm-Liouville Problems with Hilfer Derivatives. Journal of Nonlinear Modeling and Analysis. 6 (3). 775-792. doi:10.12150/jnma.2024.775
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