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 -