Date of Publication :18th August 2017

Abstract: Generalization of classical calculus that is integral calculus to non-integer order is termed as Fractional calculus. Nowadays some special mathematical functions are having greater interest from the scientists of both mathematical and scientific background. This is because of their role as solutions of fractional order differential and integral equations, as the better mathematical models of phenomena of various physical, engineering, automatization, chemical, biological, Earth science, economics etc. nature. Principle objective of this work is to implement Special Functions of Fractional calculus with the help of Graphics Processing Unit (GPU) using MATLAB. GPU Computing makes use of CPU along with GPU for faster computation. This computation speed is achieved by offloading parallel portions of numerical algorithm to GPU, while simultaneously serial portions to be executed on CPU. Error Function and Complementary Error Function are implemented on MATLAB and execution speed for both CPU computing and GPU computing are compared for faster computation. From the results it is observed that around 30X speedup is achieved in the computation of special functions using GPU.

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