In this paper, we consider the numerical inverse Laplace transform for distributed order time-fractional equations, where a discontinuous Galerkin scheme is used to discretize problem in space. The success of Talbot’s approach computation depends critically on problem’s spectral properties and present method numerically enclose spectrum compute resolvent estimates independent size. new results ...

Determining the diffusion coefficient based on the solution of the linear inverse problem of the parameter estimation by using the Least-square method is presented. A set of temperature measurements at a single sensor location inside the heat conducting body is required. The corresponding direct problem will be solved by an application of the heat fundamental solution.

The aim of this paper is to investigate an inverse problem recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such ill-posed and has important practical applications. For problem, we propose general regularization method based on the idea filter method. With suitable condition, prove that optimal under various choices pa...

In this paper, the inverse problem for identifying initial value of time-fractional diffusion wave equation on spherically symmetric region is considered. The exact solution obtained by using method separating variables and property Mittag–Leffler functions. This ill-posed, i.e. solution(if exists) does not depend measurable data. Three different kinds landweber iterative methods are used to so...

In this study, an inverse source problem for a one-dimensional timefractional diffusion equation is considered. An existence theorem based on the minimization of an error functional between the output data and the additional data is proved. Then it is showed that the unknown source function can be determined uniquely by an additional data u(0, t), 0 ≤ t ≤ T using an auxiliary uniqueness result ...