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Fractional wavelet transform through heat equation

Abstract In the present article, the authors study the heat equation in the form of the fractional wavelet transform with certain initial conditions, by exploiting the technique of fractional Fourier transform. The properties of the fundamental solution of heat equation are investigated and the relation between the fractional wavelet transform and fractional integrals obtained. The authors also study the computational aspect of the solution and heat flux of the heat equation as well as the Schrödinger equation. The graphical representations of both solutions and the heat flux for are shown and their values are compared with the classical solutions and found to have some better properties.