Fractal calculus generalizes ordinary calculus, offering a way to differentiate otherwise non-
differentiable domains and phenomena. This paper discusses the equilibrium and non …

Many phenomena in physics and engineering have fractal structures; then analysis on them
has a vital role in the application. In this chapter, we present some frameworks of analysis on …

In this paper, we summarize fractal calculus on fractal curves and nonstandard analysis.
Using nonstandard analysis which includes hyperreal and hyperinteger numbers, we define …

The C η-Calculus includes functions on fractal sets, which are not differentiable or integrable
using ordinary calculus. Sumudu transforms have an important role in control engineering …

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 …

The concept of Laplace transform has been extended to fractal curves, enabling the solution
of fractal differential equations with constant coefficients. This extension, known as the fractal …

In this paper, we give difference equations on fractal sets and their corresponding fractal
differential equations. An analogue of the classical Euler method in fractal calculus is …

In this paper, we present a generalization of diffusion on fractal combs using fractal calculus.
We introduce the concept of a fractal comb and its associated staircase function. To handle …

In this paper, we have generalized fractal calculus on fractal Cantor cubes. The mass
function on fractal Cantor cubes is defined. Then, we use the mass function to define integral …

This paper provides a framework for understanding and analyzing non-differentiable fractal
manifolds. By introducing specialized mathematical concepts and equations, such as the …