Some general properties of a fractional Sumudu transform in the class of Boehmians

In literature, there are several works on the theory and applications of integral transforms of Boehmian spaces, but fractional integral transforms of Boehmians have not yet been reported. In this paper, we investigate a fractional Sumudu transform of an arbitrary order on some space of integrable Boehmians. The fractional Sumudu transform of an integrable Boehmian is well-defined, linear and sequentially complete in the space of continuous functions. Two types of convergence are also discussed in details.