Fractional integro-differential analysis of heat and mass transfer

Application of the methods of fractional integro-differential analysis to an inhomogeneous canonical heat-conduction (diffusion) equation with inhomogeneous boundary conditions has enabled us for the first time to reduce the canonical heat-conduction equation to three equations of lower order that contain fractional-derivative operators. Examples and an analysis of those fundamental new possibilities that are opened up by such an approach to a wide class of problems of heat and mass exchange, combustion, self-propagating high-temperature synthesis, etc., have been given.