Related papers: Positive time fractional derivative
Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately…
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…
The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation…
An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
This contribution considers the time-fractional subdiffusion with a time-dependent variable-order fractional operator of order $\beta(t)$. It is assumed that $\beta(t)$ is a piecewise constant function with a finite number of jumps. A proof…
The time-fractional diffusion-wave equation is revisited, where the time derivative is of order $2 \nu$ and $0 < \nu \le 1$. The behaviour of the equation is "diffusion-like" (respectively, "wave-like") when $0 < \nu \le \frac{1}{2}$…
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…
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…
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…
A fractional diffusion equation based on Riemann-Liouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of $H$-functions. It differs from the known…
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…
The backward problem for subdiffusion equation with the fractional Riemann-Liouville time-derivative of order ? 2 (0; 1) and an arbitrary positive self-adjoint operator A is considered. This problem is ill-posed in the sense of Hadamard due…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
As it is known various dynamical processes can be modeled through the systems of time-fractional order pseudo-differential equations. In the modeling process one frequently faces with determining the adequate orders of time-fractional…
Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…