In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [−1, 1] to arbitrary complex poles outside [−1, 1]. The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrat...

Numerical methods for strongly oscillatory and singular functions are given in this paper. We present an alternative numerical solution for of oscillatory integrals of the general form Where and are smooth functions in the interval [a, b]. Also ε ω and . In order to achieve this goal and avoid singularity, the mentioned integral is solved by the modified moments using interpolating at the Cheby...

We provide a fast algorithm to compute arbitrarily many nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [−1, 1]. This algorithm is based on the derivation of explicit expressions for the Chebyshev (para-)orthogonal rational functions.

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...