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

Authors

• Sami Injrou, Department of Mathematics, Faculty of Sciences, Latakia University, Latakia, SyriaFollow
• Wadii Ali, Department of Forensic Evidence, Collage of Science, Al-Farahidy University, Baghdad, IraqFollow

Keywords

Fourier series, Fourier transform, Non-conformable fractional derivative, Non-conformable fractional integral, Fractional heat equation Mathematics Subject Classification: 26A33, 34A08, 35R11, 35S30, 42A16, 42A38

Document Type

Article

Abstract

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.

Recommended Citation

Injrou, Sami and Ali, Wadii (2026) "Solving Some Heat Problems in the Sense of the Non-Conformable Fractional Derivative by Using Modified Fourier Transform," Al-Farahidi Expert Systems Journal: Vol. 2: Iss. 1, Article 5.
DOI: https://doi.org/10.65645/3105-9104.1024

DOI

10.65645/3105-9104.1024