Related papers: Space-time fractional diffusion on bounded domains
We develop fractional buffer layers (FBLs) to absorb propagating waves without reflection in bounded domains. Our formulation is based on variable-order spatial fractional derivatives. We select a proper variable-order function so that…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
In the present work, we propose a new parameterization for the concentration flux using fractional derivatives. The fractional order differential equation in the longitudinal and vertical directions is used to obtain the concentration…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
This paper is concerned with the fractionalized diffusion equations governing the law of the fractional Brownian motion $B_H(t)$. We obtain solutions of these equations which are probability laws extending that of $B_H(t)$. Our analysis is…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated through time-space…
For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the…
We present a series of results focused on the decay in time of solutions of classical and anomalous diffusive equations in a bounded domain. The size of the solution is measured in a Lebesgue space, and the setting comprises time-fractional…
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…
In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…