Exponential operators for Fredholm singular integral equations and space fractional PDEs.

In this article, it is shown that the combined use of exponential operators and special functions provides a powerful tool to solve certain type of fractional PDEs. A system of space fractional partial differential equations is solved. It is shown that exponential operators are powerful and effective method for solving certain singular integral equations and fractional partial differential equations with non-constant coefficients. Constructive examples are also provided.