2017 December - 17 articles
The authors present a model of heat conduction using the Caputo fractional derivative with respect to time. The presented model was used to reconstruct the thermal conductivity coefficient, heat transfer coefficient, initial condition and order of fr...
In this paper, we discuss the classical pantograph equation and its generalizations to include fractional order and the higher order case. The special functions are obtained from the series solution of these equations. We study different properties o...
In this paper we construct some nonlocal operators in the Heisenberg group. Specifically, starting from the Grünwald-Letnikov derivative and Marchaud derivative in the Euclidean setting, we revisit those definitions with respect to the one of the fra...
In the option pricing literature, it is well known that (i) the decrease in the smile amplitude is much slower than the standard stochastic volatility models and (ii) the term structure of the at-the-money volatility skew is approximated by a power-l...
The extension of the fractional order derivative to the distributed order fractional derivative (DOFD) is somewhat simple from a formal point of view, but it does not yet have a simple, obvious analytic form that allows its fast numerical calculation...
In flocculation processes, particulates randomly collide and coagulate with each other, leading to the formation and sedimention of aggregates exhibiting fractal characteristics. The diffusion-limited aggregation (DLA) model is extensively employed t...
The introduction of fractional-order derivatives to epidemiological compartment models, such as SIR models, has attracted much attention. When this introduction is done in an ad hoc manner, it is difficult to reconcile parameters in the resulting fra...
A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and...
Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function. The other is prime number indexed basis entities taken from the dis...
The divergence or relative entropy between probability densities is examined. Solutions that minimise the divergence between two distributions are usually “trivial” or unique. By using a fractional-order formulation for the divergence with respect to...
Stokes’ first problem for a class of viscoelastic fluids with the generalized fractional Maxwell constitutive model is considered. The constitutive equation is obtained from the classical Maxwell stress–strain relation by substituting the first-order...
Fractional differential equations of macroeconomics, which allow us to take into account power-law memory effects, are considered. We describe an economic accelerator and multiplier with fading memory in the framework of discrete-time and continuous-...
In this paper, we study the dynamics and stability of thermistor problem for Hilfer fractional type. Classical fixed point theorems are utilized in deriving the results.
In this work, we propose a fractional complex permittivity model of dielectric media with memory. Debye’s generalized equation, expressed in terms of the phenomenological coefficients, is replaced with the corresponding differential equation by apply...
The actual state of interplay between Fractional Calculus, Signal Processing, and Applied Sciences is discussed in this paper. A framework for compatible integer and fractional derivatives/integrals in signals and systems context is described. It is...
This paper proposes the definition of fractional definite integral and analyses the corresponding fundamental theorem of fractional calculus. In this context, we studied the relevant properties of the fractional derivatives that lead to such a defini...
Fractal and Fractional are two words referring to some characteristics and fundamental problems which arise in all fields of science and technology. [...]
