@article{Sadek2025, 
author = {Lakhlifa Sadek and Ahmad Sami Bataineh and El Mostafa Sadek and Ishak Hashim},
title = {A general definition of the fractal derivative: Theory and applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {15390-15409},
keywords = {fractional derivative, ψ-fractal derivative, ψ-chain rule, ψ-fractal integral, ψ-fractal Laplace transform},
url = {https://www.sciopen.com/article/10.3934/math.2025690},
doi = {10.3934/math.2025690},
abstract = {In this paper, we introduce a general definition of the fractal derivative with respect to a function    ψ, in the context of the order    0  <  α  ≤  1 and the function    ψ  (  Θ  ). This novel definition generalizes the classical fractal derivative, which is recovered when    ψ  (  Θ  )  =  Θ, as described in previous works by Chen et al. [1,2]. We explored key properties of the    ψ-fractal derivative, including the    ψ-fractal Laplace transform, which provides a powerful tool for solving complex differential equations in fractal domains. We also derived a generalized    ψ-chain rule, extending classical calculus into the fractal domain, and presented fundamental operations related to this unique derivative. We give some applications.}
}