Solving Some Heat Problems in the Sense of the Non-Conformable Fractional Derivative by Using Modified Fourier Transform

In this paper, we present two new concepts in Fourier analysis: the Fourier series and the Fourier transform in the sense of non-conformable fractional calculus. Some of their main properties are proven. Using this new Fourier series, new approximations of some functions are given, a frequency spectrum of a signal is plotted, and several cases of the heat equations involving the time non-conformable fractional derivative are solved and graphically presented. Furthermore, the introduced new Fourier transform is used to solve a homogeneous space-time non-conformable fractional heat equation.