Research article

Theory of discrete fractional Sturm–Liouville equations and visual results

  • Received: 11 March 2019 Accepted: 09 May 2019 Published: 03 June 2019
  • MSC : Primary: 34A08, 39A70, 34B24, 28A75; Secondary: 44A10

  • In this article, we study discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Grünwald-Letnikov fractional operators with both delta and nabla operators. Self-adjointness of the DFSL operator is analyzed and fundamental spectral properties are proved. Besides, we get sum representation of solutions for DFSL problem by means of Laplace transform for nabla fractional difference equations and find the analytical solutions of the problem. Moreover, the results for DFSL problem, discrete Sturm-Liouville (DSL) problem with the second order, and fractional Sturm-Liouville (FSL) problem are compared with the second order classical Sturm-Liouville (CSL) problem. We display the results comparatively by tables and figures.

    Citation: Erdal Bas, Ramazan Ozarslan. Theory of discrete fractional Sturm–Liouville equations and visual results[J]. AIMS Mathematics, 2019, 4(3): 593-612. doi: 10.3934/math.2019.3.593

    Related Papers:

  • In this article, we study discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Grünwald-Letnikov fractional operators with both delta and nabla operators. Self-adjointness of the DFSL operator is analyzed and fundamental spectral properties are proved. Besides, we get sum representation of solutions for DFSL problem by means of Laplace transform for nabla fractional difference equations and find the analytical solutions of the problem. Moreover, the results for DFSL problem, discrete Sturm-Liouville (DSL) problem with the second order, and fractional Sturm-Liouville (FSL) problem are compared with the second order classical Sturm-Liouville (CSL) problem. We display the results comparatively by tables and figures.


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