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M\"untz Sturm-Liouville Problems: Theory and Numerical Experiments
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This paper presents two new classes of M\"untz functions which are called Jacobi-M\"untz 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 M\"untz 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.
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Cited by 1 Pith paper
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M\"untz Pseudo Spectral Method: Theory and Numerical Experiments
Two new non-classical Lagrange basis families are introduced for Müntz pseudo-spectral methods, with error bounds, Erdélyi-Kober fractional differentiation matrices, and numerical tests.
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