Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator

TL;DR

This paper studies inverse problems for a fractional diffusion equation involving the Dzherbashian-Nersesian operator, establishing existence and uniqueness results that generalize previous findings in fractional calculus.

Contribution

It introduces the fractional Dzherbashian-Nersesian operator and derives conditions for solving inverse source problems in fractional diffusion equations.

Findings

Laplace transform expression for the Dzherbashian-Nersesian operator derived

Existence and uniqueness of solutions for inverse problems established

Results generalize several known fractional diffusion equations

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.