Reconstruction of an order of derivative and a source term in a fractional diffusion equation from final measurements

J Janno, N Kinash - Inverse Problems, 2018 - iopscience.iop.org
An inverse problem to recover a space-dependent factor of a source term and an order of a
time derivative in a fractional diffusion equation from final data is considered. The …

[PDF][PDF] Determination of the order of fractional derivative and a kernel in an inverse problem for a generalized time fractional diffusion equation

J Janno - Electron. J. Differential Equations, 2016 - ejde.math.txstate.edu
A generalized time fractional diffusion equation containing a lower order term of a
convolutional form is considered. Inverse problem to determine the order of a fractional …

Landweber iterative method for identifying a space-dependent source for the time-fractional diffusion equation

F Yang, YP Ren, XX Li, DG Li - Boundary Value Problems, 2017 - Springer
This paper is devoted to identifying an unknown source for a time-fractional diffusion
equation with variable coefficients in a general bounded domain. This is an ill-posed …

[PDF][PDF] Identification of an unknown source term for a time fractional fourth-order parabolic equation

S Aziz, SA Malik - Electron. J. Differ. Equ, 2016 - kurims.kyoto-u.ac.jp
In this article, we considered two inverse source problems for fourth-order parabolic
differential equation with fractional derivative in time. Determination of a space dependent …

Inverse problems for a perturbed time fractional diffusion equation with final overdetermination

N Kinash, J Janno - Mathematical Methods in the Applied …, 2018 - Wiley Online Library
Inverse problems to recover a space‐dependent factor of a source term and an initial
condition in a perturbed time fractional diffusion equation containing an additional …

Inverse problem with a time‐integral condition for a fractional diffusion equation

H Lopushanska, A Lopushansky - Mathematical Methods in the …, 2019 - Wiley Online Library
We find the conditions for the unique solvability of the inverse problem for a time‐fractional
diffusion equation with Schwarz‐type distributions in the right‐hand sides. This problem is to …

Inverse problems for a generalized fractional diffusion equation with unknown history

J Janno - arXiv preprint arXiv:2402.00482, 2024 - arxiv.org
Inverse problems for a diffusion equation containing a generalized fractional derivative are
studied. The equation holds in a time interval $(0, T) $ and it is assumed that a state $ u …

Inverse problems for a time fractional diffusion equation in the Schwartz‐type distributions

H Lopushanska, A Lopushansky - Mathematical Methods in the …, 2021 - Wiley Online Library
We find the conditions for the unique solvability of the inverse problem of the solution's initial
data determination for a time fractional diffusion equation with a Schwartz‐type distribution …

Inverse problems with unknown boundary conditions and final overdetermination for time fractional diffusion-wave equations in cylindrical domains

J Janno - Mathematics, 2021 - mdpi.com
Inverse problems to reconstruct a solution of a time fractional diffusion-wave equation in a
cylindrical domain are studied. The equation is complemented by initial and final conditions …

[PDF][PDF] An inverse fractional source problem in a space of periodic spatial distributions

A Lopushansky, H Lopushanska, O Myaus - Fractional differ. calc, 2016 - files.ele-math.com
For a time fractional diffusion equation and diffusion-wave equation with Caputo partial
derivatives we prove the correctness of an inverse problem. This problem is to find a solution …