In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of paper is to establish properties weak solutions initial-boundary value problem, such as existence, uniqueness and regularity estimates. Moreover, apply obtained theories an inverse source problem. problem under boundary measurements proved.

In this paper, we obtain the sharp uniqueness for an inverse $ x $-source problem a one-dimensional time-fractional diffusion equation with zeroth-order term by minimum possible lateral Cauchy data. The key ingredient is unique continuation which holds weak solutions.

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to e...

In this article, we study an inverse problem to determine an unknown source term in a space time fractional diffusion equation, whereby the data are obtained at a certain time. In general, this problem is ill-posed in the sense of Hadamard, so the Fourier truncation method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules a...

This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation FADE on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regul...

This research determines an unknown source term in the fractional diffusion equation with Riemann–Liouville derivative. problem is ill-posed. Conditional stability for inverse can be given. Further, a Tikhonov regularization method was applied to regularize problem. In theoretical results, we propose priori and posteriori parameter choice rules obtain convergence estimates.

This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining mild solution, we establish fundamental unique existence, limited smoothing property and long-time asymptotic behavior which mostly inherit those single equation. Owing to coupling effect, also obtain uniqueness an inverse on determining all fractional orde...

This article is devoted to the study of an inverse source problem for a mixed type equation with fractional diffusion in parabolic part and wave hyperbolic cylindrical domain. The solution obtained form FourierBessel series expansion using orthogonal set Bessel functions. theorems uniqueness existence are proved.

In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary and conditions. Some properties of eigenvalues eigenfunctions are investigated. Asymtotic representation eigenfunction obtained. Reconstruction the shown by Weyl function.