Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator
Analysis of PDEs
2021-11-09 v1
Abstract
Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives namely Riemann-Liouville, Caputo and Hilfer derivatives are shown to be special cases of the earlier one. The expression for Laplace transform of fractional Dzherbashian-Nersesian operator is constructed. Inverse problems of recovering space dependent and time dependent source terms of a time fractional diffusion equation with involution and involving fractional Dzherbashian-Nersesian operator are considered. The results on existence and uniqueness for the solutions of inverse problems are established. The results obtained here generalize several known results.
Cite
@article{arxiv.2105.05040,
title = {Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator},
author = {Anwar Ahmad and Muhammad Ali and Salman A. Malik},
journal= {arXiv preprint arXiv:2105.05040},
year = {2021}
}