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 study, a new generalized local fractal derivative operator is introduced and we
discuss its implications in classical systems through the Lagrangian and Hamiltonian …

In this paper, we give a brief summary of fractal calculus. Fractal functional differential
equations are formulated as a framework that provides a mathematical model for the …

Our main goal in this long survey article is to provide an overview of the theory of complex
fractal dimensions and of the associated geometric or fractal zeta functions, first in the case …

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

In this paper, we explore the intriguing field of fractal calculus as it pertains to fractal curves
and fractal sets. Our study includes an exploration of the method analogues of the separable …

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 …

In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of
fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is …

Abstract Fractal analogue of Newton, Lagrange, Hamilton, and Appell's mechanics are
suggested. The fractal α-velocity and α-acceleration are defined in order to obtain the …