Corpus ID: 199064629

# M\"untz Sturm-Liouville Problems: Theory and Numerical Experiments

@inproceedings{KhosravianArab2019MuntzSP,
title={M\"untz Sturm-Liouville Problems: Theory and Numerical Experiments},
author={Hassan Khosravian-Arab and Mohammad Reza Eslahchi},
year={2019}
}
• Published 31 July 2019
• Mathematics, Computer Science
This paper presents two new classes of Müntz functions which are called JacobiMüntz 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…

#### References

SHOWING 1-10 OF 28 REFERENCES
Fractional Sturm-Liouville problem
• Computer Science, Mathematics
Comput. Math. Appl.
• 2013
It is shown that the Legendre Polynomials resulting from an FLE are the same as those obtained from the integer order Legendre equation; however, the eigenvalues of the two equations differ.
Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation
• Mathematics, Computer Science
J. Comput. Phys.
• 2013
It is proved that the eigenvalues of the singular problems are real-valued and the corresponding eigenfunctions are orthogonal, hence completing the whole family of the Jacobi poly-fractonomials.
Generalized Jacobi functions and their applications to fractional differential equations
• Mathematics, Computer Science
Math. Comput.
• 2016
In this paper, we consider spectral approximation of fractional dif- ferential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi functions (GJFs),
Fractional Sturm-Liouville boundary value problems in unbounded domains: Theory and applications
• Mathematics, Computer Science
J. Comput. Phys.
• 2015
It is proved that these fractional Sturm-Liouville operators are self-adjoint and the obtained eigenvalues are all real, the corresponding eigenfunctions are orthogonal with respect to the weight function associated to F SLOs-1 and FSLOs-2 and form two sets of non-polynomial bases.
A Petrov-Galerkin Spectral Method of Linear Complexity for Fractional Multiterm ODEs on the Half Line
• Mathematics, Computer Science
SIAM J. Sci. Comput.
• 2017
We present a new tunably accurate Laguerre Petrov--Galerkin spectral method for solving linear multiterm fractional initial value problems with derivative orders at most one and constant coefficients
A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• Mathematics, Computer Science
SIAM J. Numer. Anal.
• 2018
This work considers the one-dimensional diffusion equation with general two-sided fractional derivative characterized by a parameter p, and derives (two-sided) Jacobi polyfracnomials as eigenfunctions of a Sturm--Liouville problem with weights uniquely determined by the parameter p.
Petrov-Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations
• Mathematics, Physics
SIAM J. Sci. Comput.
• 2017
This work develops two spectrally-accurate schemes, namely a Petrov-Galerkin spectral method and a spectral collocation method for distributed order fractional differential equations, based on the fractional Sturm-Liouville eigen-problems (FSLPs).
On a Differential Equation with Left and Right Fractional Derivatives
• Mathematics
• 2007
We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational
Nonpolynomial collocation approximation of solutions to fractional differential equations
• Mathematics
• 2013
We propose a non-polynomial collocation method for solving fractional differential equations. The construction of such a scheme is based on the classical equivalence between certain fractional
Tempered Fractional Sturm-Liouville EigenProblems
• Mathematics, Computer Science
SIAM J. Sci. Comput.
• 2015
This study introduces two classes of regular and singular tempered fractional Sturm--Liouville problems of two kinds (TFSLP-I and TF SLP-II) of order $\nu \in (0,2)$.