TY - JOUR ID - 13049 TI - Local fractal Fourier transform and applications JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Khalili Golmankhaneh, Alireza AU - Ali, Karmina Kamal AU - Yilmazer, Resat AU - Kaabar, Mohammed Khalid Awad AD - Department of Physics Islamic Azad University, Urmia Branch Urmia, Iran. AD - Faculty of Science, Department of Mathematics, University of Zakho, Iraq. AD - Faculty of Science, Department of Mathematics, Firat University, Elazig, Turkey. AD - Department of Mathematics and Statistics, Washington State University, Pullman, WA, USA. Y1 - 2022 PY - 2022 VL - 10 IS - 3 SP - 595 EP - 607 KW - Fractal calculus KW - fractal local Fourier transform KW - fractal differential equation KW - fractal Fourier Convolution theorem KW - fractal Dirac delta function DO - 10.22034/cmde.2021.42554.1832 N2 - In this manuscript, we review fractal calculus and the analogues of both local Fourier transform with its related properties and Fourier convolution theorem are proposed with proofs in fractal calculus. The fractal Dirac delta with its derivative and the fractal Fourier transform of the Dirac delta is also defined. In addition, some important applications of the local fractal Fourier transform are presented in this paper such as the fractal electric current in a simple circuit, the fractal second order ordinary differential equation, and the fractal Bernoulli-Euler beam equation. All discussed applications are closely related to the fact that, in fractal calculus, a useful local fractal derivative is a generalized local derivative in the standard calculus sense. In addition, a comparative analysis is also carried out to explain the benefits of this fractal calculus parameter on the basis of the additional alpha parameter, which is the dimension of the fractal set, such that when α = 1, we obtain the same results in the standard calculus.  UR - https://cmde.tabrizu.ac.ir/article_13049.html L1 - https://cmde.tabrizu.ac.ir/article_13049_dc2ffbc2729ed53148807a978137b821.pdf ER -