Fractional calculus is a field with growing interest for researchers due to
its applications in the various fields like mathematical modeling, control systems,
image processing, financial systems, etc. Special mathematical functions like
Gamma functions, Mittag-Leffler function, Hypergeometric function, etc. play a
crucial role in the analytical and numerical solutions of fractional differential
equations. However, the numerical computation of these functions is a tedious and
time-consuming task. This is due to the fact that these functions do not have
straightforward definitions and are mostly represented by series expansions. This
chapter attempts to exploit the parallel computing power of Graphics Processing
Unit (GPU) for computing some of the well-known special functions used in
fractional calculus. Using the numerical computational platform of MATLAB and
its parallel computing toolbox, the chapter reports the use of GPU hardware to
compute these functions using their series definitions. It is shown with the help of
various case studies and for different parameter combinations that the
implementation of parallel computation of special functions reduces the execution
time. A comparative study showing the effect of function parameters on their
parallel computation is also presented.
Keywords: Fractional Calculus, Special Functions, Parallel computation, GPU
Computing.
