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Müntz sturm-liouville problems: Theory and numerical experiments

  • Hassan Khosravian-Arab and Mohammad Reza Eslahchi EMAIL logo
Published/Copyright: June 23, 2021
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 24 Issue 3

Abstract

This paper presents two new classes of Müntz functions which are called Jacobi-Müntz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they have some spectral properties such as: orthogonality, completeness, three-term recurrence relations and so on. With respect to these functions two new orthogonal projections and their error bounds are derived. Also, two new Müntz type quadrature rules are introduced. As two applications of these basis functions some fractional ordinary and partial differential equations are considered and numerical results are given.

Keywords: Erdélyi-Kober fractional derivatives and integrals; fractional Sturm-Liouville problems; Müntz functions; self-adjoint operator; spectral properties; orthogonal projections; error bounds; Müntz quadrature rules; fractional ordinary and partial differential equations
MSC 2010: Primary 26A33; 33C45; 65M70; Secondary 34L10; 41A55

Acknowledgements

The authors would like to express their special thanks to Prof. Virginia Kiryakova: Editor-in-Chief, for helps, supports, and her valuable comments which greatly improved the quality of this manuscript. The authors also wish to thank the anonymous reviewers for their helpful comments and suggestions.

Finally, the authors would like to acknowledge the financial support of the Iran National Science Foundation (INSF) (Grant No. 96014450).

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Received: 2019-12-31
Revised: 2021-05-08
Published Online: 2021-06-23
Published in Print: 2021-06-25

© 2021 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial Survey
  3. In memory of the honorary founding editors behind the FCAA success story
  4. Research Paper
  5. Short time coupled fractional fourier transform and the uncertainty principle
  6. (N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
  7. Sharp asymptotics in a fractional Sturm-Liouville problem
  8. Multi-term fractional integro-differential equations in power growth function spaces
  9. Galerkin method for time fractional semilinear equations
  10. Müntz sturm-liouville problems: Theory and numerical experiments
  11. Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂tβ u = −(− Δ)α/2 u − (− Δ)γ/2 u
  12. Nonlinear convolution integro-differential equation with variable coefficient
  13. An efficient localized collocation solver for anomalous diffusion on surfaces
  14. Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach
  15. Sliding methods for the higher order fractional laplacians
  16. Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices
https://doi.org/10.1515/fca-2021-0034
Keywords for this article
Erdélyi-Kober fractional derivatives and integrals; fractional Sturm-Liouville problems; Müntz functions; self-adjoint operator; spectral properties; orthogonal projections; error bounds; Müntz quadrature rules; fractional ordinary and partial differential equations

Articles in the same Issue

  1. Frontmatter
  2. Editorial Survey
  3. In memory of the honorary founding editors behind the FCAA success story
  4. Research Paper
  5. Short time coupled fractional fourier transform and the uncertainty principle
  6. (N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
  7. Sharp asymptotics in a fractional Sturm-Liouville problem
  8. Multi-term fractional integro-differential equations in power growth function spaces
  9. Galerkin method for time fractional semilinear equations
  10. Müntz sturm-liouville problems: Theory and numerical experiments
  11. Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂tβ u = −(− Δ)α/2 u − (− Δ)γ/2 u
  12. Nonlinear convolution integro-differential equation with variable coefficient
  13. An efficient localized collocation solver for anomalous diffusion on surfaces
  14. Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach
  15. Sliding methods for the higher order fractional laplacians
  16. Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices
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