Fractal and Fractional, Volume 2, Issue 1

In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results t...

An attempt is made to identify the orders of the fractional derivatives in a simple anomalous diffusion model, starting from real data. We consider experimental data taken at the Columbus Air Force Base in Mississippi. Using as a model a one-dimensio...

We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approxima...

The question addressed by this paper is tackled through a continuum micromechanics model of a 2D random checkerboard, in which one phase is linear elastic and another linear viscoelastic of integer-order. The spatial homogeneity and ergodicity of the...

A fractional-calculus-based model is used to analyze the data obtained from the image analysis of mixtures of olive and soybean oil, which were quantified with the RGB color system. The model consists in a linear fractional differential equation, con...

This paper considers the Freedman model using the Liouville–Caputo fractional-order derivative and the fractional-order derivative with Mittag–Leffler kernel in the Liouville–Caputo sense. Alternative solutions via Laplace transform, Sumudu–Picard an...

Cerebral aneurysms and microaneurysms are abnormal vascular dilatations with high risk of rupture. An aneurysmal rupture could cause permanent disability and even death. Finding and treating aneurysms before their rupture is very difficult since symp...

Anomalous deviations from the Beer-Lambert law have been observed for a long time in a wide range of application. Despite all the attempts, a reliable and accepted model has not been provided so far. In addition, in some cases the attenuation of radi...

Peer review is an essential part in the publication process, ensuring that Fractal and Fractional maintains high quality standards for its published papers. In 2017, a total of 17 papers were published in the journal. Thanks to the cooperation of our...

Fractional extensions of the cable equation have been proposed in the literature to describe transmembrane potential in spiny dendrites. The anomalous behavior has been related in the literature to the geometrical properties of the system, in particu...

Singular functions and, in general, Hölder functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocities as tools to characterize Hölder and singular fun...

The control of thermal interfaces has gained importance in recent years because of the high cost of heating and cooling materials in many applications. Thus, the main focus in this work is to compare the second and third generations of the CRONE cont...

Recently, fractional differential equations (FDEs) have attracted much more attention in modeling real-life problems. Since most FDEs do not have exact solutions, numerical solution methods are used commonly. Therefore, in this study, we have demonst...

We study the convergence of the parameter family of series: $V_{\alpha ,\beta }(t)={\sum }_p{p}^{-\alpha }\exp (2\pi i{p}^{\beta }t)$ , $\alpha ,\beta \in {\mathbb{R}}_{>0},t\in [0,1)$ defined over prime numbers p and, subsequently, their differentiability...

The dust aerosols floating in the atmosphere of Mars cause an attenuation of the solar radiation traversing the atmosphere that cannot be modeled through the use of classical diffusion processes. However, the definition of a type of fractional diffus...