Müntz sturm-liouville problems: Theory and numerical experiments
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Hassan Khosravian-Arab
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.
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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© 2021 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Survey
- In memory of the honorary founding editors behind the FCAA success story
- Research Paper
- Short time coupled fractional fourier transform and the uncertainty principle
- (N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
- Sharp asymptotics in a fractional Sturm-Liouville problem
- Multi-term fractional integro-differential equations in power growth function spaces
- Galerkin method for time fractional semilinear equations
- Müntz sturm-liouville problems: Theory and numerical experiments
- Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂tβ u = −(− Δ)α/2 u − (− Δ)γ/2 u
- Nonlinear convolution integro-differential equation with variable coefficient
- An efficient localized collocation solver for anomalous diffusion on surfaces
- Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach
- Sliding methods for the higher order fractional laplacians
- Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices
Artikel in diesem Heft
- Frontmatter
- Editorial Survey
- In memory of the honorary founding editors behind the FCAA success story
- Research Paper
- Short time coupled fractional fourier transform and the uncertainty principle
- (N + α)-Order low-pass and high-pass filter transfer functions for non-cascade implementations approximating butterworth response
- Sharp asymptotics in a fractional Sturm-Liouville problem
- Multi-term fractional integro-differential equations in power growth function spaces
- Galerkin method for time fractional semilinear equations
- Müntz sturm-liouville problems: Theory and numerical experiments
- Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation ∂tβ u = −(− Δ)α/2 u − (− Δ)γ/2 u
- Nonlinear convolution integro-differential equation with variable coefficient
- An efficient localized collocation solver for anomalous diffusion on surfaces
- Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach
- Sliding methods for the higher order fractional laplacians
- Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices
