Convolution Theorems for Fractional Fourier Cosine and Sine Transforms and Their Extensions to Boehmians

By introducing two fractional convolutions, we obtain the convolution theorems for fractional Fourier cosine and sine transforms. Applying these convolutions, we construct two Boehmian spaces and then we extend the fractional Fourier cosine and sine transforms from these Boehmian spaces into another Boehmian space with desired properties.