Related papers: Generalised Fractional Evolution Equations of Capu…
In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion,…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
A well-posedness result for a time-shift invariant class of evolutionary operator equations involving material laws with fractional time-integrals of order $\alpha\in]0,1[$ is considered and exemplified by an application to a Kelvin-Voigt…
We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the…
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
We show that the anomalous diffusion equations with a fractional derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the L\'evy stable distributions which stem from the evolution properties…
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that…
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in…
We propose an extension of the cable equation by introducing a Caputo time fractional derivative. The fundamental solutions of the most common boundary problems are derived analitically via Laplace Transform, and result be written in terms…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
This work is dedicated to the study of a mixed-type partial differential equation involving a Caputo fractional derivative in the time domain $t > 0$ and a classical parabolic equation in the domain $t < 0$, along with Dezin-type non-local…
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
The aim of this work is to present, in self-contained form, results concerning fundamental and the most important questions related to linear stochastic Volterra equations of convolution type. The paper is devoted to study the existence and…
Space time fractional nonlinear evolution equations have been widely applied for describing various types of physical mechanism of natural phenomena in mathematical physics and engineering. The proposed generalized exp expansion method…
In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator.…
We consider diffusion type equations with a distributed order derivative in the time variable. This derivative is defined as the integral in $\alpha$ of the Caputo-Dzhrbashian fractional derivative of order $\alpha \in (0,1)$ with a certain…
By observing that the fractional Caputo derivative can be expressed in terms of a multiplicative convolution operator, we introduce and study a class of such operators which also have the same self-similarity property as the Caputo…
We consider fractional generalizations of the ordinary differential equation that governs the creep phenomenon. Precisely, two Caputo fractional Voigt models are considered: a rheological linear model and a nonlinear one. In the linear…
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…