Current Developments in Mathematical Sciences

Current Developments in Mathematical Sciences

Volume: 1

Frontiers in Fractional Calculus

This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics ...
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GPU Computing of Special Mathematical Functions used in Fractional Calculus

Pp. 199-232 (34)

Parag Patil, Navin Singhaniya, Chaitanya Jage, Vishwesh A. Vyawahare, Mukesh D. Patil and P.S.V. Nataraj

Abstract

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.

Affiliation:

Department of Electronics Engineering, Ramrao Adik Institute of Technology, D. Y. Patil Vidyanagar, Nerul, Navi Mumbai 400 706, India.