MUNTZ STURM-LIOUVILLE PROBLEMS: THEORY AND NUMERICAL EXPERIMENTS

This paper presents two new classes of Muntz functions which are called Jacobi-Muntz 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 Muntz 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.