Kilbas Saigo

Kilbas and Saigo Function: Computes the Kilbas-Saigo function in terms of the parameters alpha and beta with desired accuracy. This function was used in the paper, ”Fractional Order Complexity Model of the Diffusion Signal Decay in MRI” by Richard L Magin, Hamid Karani, Shuhong Wang and Yingjie Liang, (Mathematics 2019, 7, 348 (16 pages); doi:10.3390/math7040348). The Kilbas-Saigo model is defined by Equations (5) and (8) in the paper, ”Fractional Models of Anomalous Relaxation Based on the Kilbas and Saigo Function,” by E. Capelas de Oliveira, F. Mainardi, and J. Vaz Jr. and published in the journal, Meccanica 2014, Volume 49, Issue 9, pp 2049-2060. The computation utilizes MATLAB’s variable-precision floating-point arithmetic (VPA). The number of terms needed in the power series is set by the accuracy specified for the input parameter ’eps0’. This version of the Kilbas-Saigo function is monotonically decreasing for alpha + beta < 1.