Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractio...

In this paper an inverse problem for the space fractional heat conduction equation is investigated. Firstly, we describe the approximate solution of the direct problem. Secondly, for the inverse problem part, we define the functional illustrating the error of approximate solution. To recover the thermal conductivity coefficient we need to minimize this functional. In order to minimize this func...

In this paper, we consider the inverse source problem for time-fractional diffusion equation, which has been known to be an ill-posed problem. To deal with ill-posedness of problem, propose transform into a regularized L^2 and total variational (TV) regularization terms. Differing from classical Tikhonov penalty terms, TV is beneficial reconstructing discontinuous or piecewise constant solution...

In this study, we considered a fractional parabolic equation for identifying the unknown diffusion coefficient from noisy measurement of ultimate time solution. It is an inverse problem involving nonlocal operator that nonlinear and poorly formulated. By demonstrating existence singular solution with regard to final observed data, demonstrate identifiability problem. The expressed as regularize...