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We study the higher-order heat-type equation with first time and M-th spatialpartial derivatives, M = 2, 3, ... . We demonstrate that its exact solutionsfor M even can be constructed with the help of signed Levy stable functions.For M odd the same role is played by a special generalization of Airy Aifunction that we introduce and study. This permits one to generate the exactand explicit heat kernels pertaining to these equations. We examineanalytically and graphically the spacial and temporary evolution of particularsolutions for simple initial conditions.

The Higher-Order Heat-Type Equations via signed L\'{e}vy stable and generalized Airy functions