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.

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

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...

time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. the stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. it is well-known that the stabi...

In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on boundary. We prove unique recovery together with their weights, which does not require full knowledge domain or medium properties, e.g. and potential coefficients, initial condition source model. The proof is based Laplace transform asy...

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...

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.