In this paper, we are interested in the problem of determining source function for Sobolev equation with fractional Laplacian. This is ill-posed sense Hadamard. order to edit instability solution, applied Landweber method. theoretical analysis results, show error estimate between exact solution and regularized by using an a priori regularization parameter choice rule posteriori rule. Finally, i...

We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. determine both the conductivity absorption coefficient from exterior partial measurements of Dirichlet-to-Neumann map. Our approach relies on time-integral transform technique as well unique continuation property operator.

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

The solvability of the fractional partial differential equation with integral overdetermination condition for an inverse problem is investigated in this paper. We analyze direct solution by using “energy inequality” method. Using fixed point technique, existence and uniqueness on data are established.

We establish that the potential appearing in a fractional Schrödinger operator is uniquely determined by an internal spectral data.

We consider a one-dimensional fractional diffusion equation: ∂α t u(x, t) = ∂ ∂x ( p(x) ∂u ∂x (x, t) ) , 0 < x < `, where 0 < α < 1 and ∂α t denotes the Caputo derivative in time of order α. We attach the homogeneous Neumann boundary condition at x = 0, ` and the initial value given by the Dirac delta function. We prove that α and p(x), 0 < x < `, are uniquely determined by data u(0, t), 0 < t ...