Fractal and Fractional, Volume 3, Issue 1

In recent years, intrinsic metrics have been described on various fractals with different formulas. The Sierpinski gasket is given as one of the fundamental models which defined the intrinsic metrics on them via the code representations of the points...

In this paper, authors the present the discovery of an interesting identity regarding trapezium-type integral inequalities. By using the lemma as an auxiliary result, some new estimates with respect to trapezium-type integral inequalities via general...

In this paper, fractal stochastic Langevin equations are suggested, providing a mathematical model for random walks on the middle- $\tau$ Cantor set. The fractal mean square displacement of different random walks on the middle- $\tau$ Cantor...

In this paper, we use concepts of q-calculus to introduce a certain type of q-difference operator, and using it define some subclasses of analytic functions. Inclusion relations, coefficient result, and some other interesting properties of these clas...

In this paper, the approximated analytical solution for the fractional Swift–Hohenberg (S–H) equation has been investigated with the help of the residual power series method (RPSM). To ensure the applicability and efficiency of the propos...

The major problem in the process of mixing fluids (for instance liquid-liquid mixers) is turbulence, which is the outcome of the function of the equipment (engine). Fractal mixing is an alternative method that has symmetry and is predictable. Therefo...

This paper reviews the implementation of fractal based image interpolation, the associated visual artifacts of the interpolated images, and various techniques, including novel contributions, that alleviate these awkward visual artifacts to achieve vi...

Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of these sets for dynamical systems over the hyperbolic numbers. Hyperbolic n...

Let f be analytic in open unit disc $E=\{z:|z|<1\}$ with $f\left(0\right)=0$ and $f^{{}^{\prime }}\left(0\right)=1$ . The q-derivative of f is defined by: $D_{q}f\left(z\right)=\frac{f\left(z\right)-f\left(qz\right)}{(1-q)z},q\&i$...

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral repre...

In this research, the fractal structure of beads of different sizes obtained by the spray-drying of aqueous dispersions of microcrystalline cellulose (MCC) was studied. These beads were formed as a result of the aggregation of rod-shaped cellulose na...

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This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived. The equivalence with t...